Grating Assisted Directional Coupler (GADC) is an important optical waveguide device because it is capable of achieving efficient coupling between the two modes having mismatched phase. GADC provides a new way to improve the performances of the coupler and the grating. Due to its compact structure, easy integration, versatility, and good wavelength selectivity, GADC is now widely used in various scenarios, such as codirectional coupler, optical add-drop filter, tunable delay line, wavelength division multiplexer, mode division multiplexer, filter, mode filter, and so on. However, most of these devices do not have tunability, while tunability is the key for improving the device performance, realizing device reconfiguration, and enlarging the device fabrication tolerance. Up to now, the tunability of optical waveguide devices are usually realized based on the Electro-Optic (EO) and the Thermo-Optic (TO) effects. Among them, EO tuning is more fascinating due to its high tuning speed and low power consumption. Lithium Niobite (LN) On Insulator (LNOI), a newly emerging integrated optics platform in recent years, not only keeps the excellent EO, acousto-optic, and nonlinear optical properties of LN, but also enables high-index-contrast and hence high-confinement waveguide, which makes it an excellent platform for developing compact and high-performance EO devices.In this paper, a high-performance electro-optical tunable GADC in LNOI is proposed and demonstrated. Our proposed device consists of an Asymmetric Directional Coupler (ADC), a sidewall Long Period Waveguide Grating (LPWG), and a set of electrodes. The ADC is composed of a Single-Mode Waveguide (SMW) and a Two-Mode Waveguide (TMW), and both are rib waveguides with identical etch depth. The LPWG is formed on the inner side of the ridge of the TMW. Both ADC and the LPWG are formed with the Inductively Coupled Plasma (ICP) process simultaneously. Due to the large birefringence of LN, the LPWG can not meet the phase matching of the two polarized fundamental modes in the SMW and the TMW simultaneously, thus it is designed only for the coupling of the E${}_{\mathrm{11}\mathrm{T}}^z$ and E${}_{\mathrm{11}\mathrm{S}}^z$modes. To employ the maximum EO coefficient γ₃₃ of LN, a 600-nm thick x-cut LN wafer and y-propagation layout are adopted. And Titanium (Ti) gold electrodes are placed both sides of the TMW to provide EO tuning. Here, to avoid the light absorption induced by the metal electrode, a Silicon Dioxide (SiO₂) buffer layer is formed on the LNOI waveguides to isolate the waveguides from the electrodes. In this work, the width of the SMW and the TMW are set to 1.2 μm and 2.0 μm, respectively, the space between them is set to 0.7 μm, and the etch depth is set to 200 nm. With these data, the grating period is 48.0 μm at the resonant wavelength of 1 550 nm and the grating length is 816 μm, corresponding to 17 grating periods, calculated by using the beam propagation method (Rsoft) to simulate the light propagation through the grating when the grating duty cycle is set to 50%.We fabricated dozens of GADCs with somewhat different periods on a single x-cut LNOI chip. When the E${}_{\mathrm{11}\mathrm{T}}^z$mode is excited in the TMW, the transmission spectrum of the TMW exhibits a distinct rejection band with a maximum contrast of 14.8 dB at the center wavelength 1 595.3 nm, while the output spectrum of the SMW exhibits somewhat complementary pass-band. This indicates that the E${}_{\mathrm{11}\mathrm{T}}^z$ mode of the TMW is coupled into the E${}_{\mathrm{11}\mathrm{S}}^z$ mode of the SMW near the rejection band. In addition, when the E${}_{\mathrm{11}\mathrm{S}}^z$mode is excited in the SMW, the output spectrum of the SMW exhibits a distinct rejection band with an isolation of 13.6 dB at the wavelength of 1 595.3 nm, while the spectrum output from the TMW exhibits a distinct complementary pass-band near the rejection band, indicating an efficient coupling from the E${}_{\mathrm{11}\mathrm{S}}^z$ mode of the SMW to the E${}_{\mathrm{11}\mathrm{T}}^z$mode of the TMW.To facilitate the investigation of the EO and TO tunability of the device, we further packaged GADC unit on the chip. The two ends of the TMW and the SMW of GADC were pigtailed with 3.2 μm UHNAF fiber arrays (with two fibers) using UV glue. The measured results show that the central wavelength of the rejection band of the TMW transmission spectrum redshifts from 1 595.3 nm to 1 599.0 nm as the tuning voltage increases from 0 V to 10 V, the maximum contrast of 14.8 dB at the center wavelength 1 595.3 nm. While the center wavelength of the rejection band moves from 1 595.3 nm to 1 592.3 nm as the tuning voltage changes from 0 V to -8 V, and the isolation reaches its maximum value of 20.7 dB at -2 V. The EO tuning efficiencies are 0.38 nm/V (1 592.3~1 599.0 nm). Similarly, the center wavelength of the rejection band of the SMW transmission spectrum moves from 1 595.3 nm to 1 597.9 nm as the tuning voltage changes from 0 V to 9 V and the isolation reaches its maximum value of 18.4 dB at -2 V. The EO tuning efficiencies is 0.29 nm/V.Finally, the TO tuning feature of the packaged GADC was also evaluated by investigating the shift of the center wavelength of the rejection band in the TMW transmission spectrum with the change of the ambient temperature. The center wavelength of the rejection band redshifts from 1 595.3 nm to 1 598.8 nm when the ambient temperature changes from 25 ℃ to 50 ℃. The TO tuning efficiency is 0.14 nm/℃. Our proposed LNOI GADC can find applications in the fields of high-speed tunable wavelength filtering, mode filtering, and EO modulation.