The fields of high-performance optical signal processing, optical computing, microwave photonics, and high-speed optical communications are important directions for photonics research. In these systems, dispersion compensation is a key technology to eliminate signal distortion and improve signal quality. Typical dispersion compensation usually has three methods: first, the use of dispersion-compensated optical fibres, whose technical advantage lies in the fact that very large dispersion values can be obtained and both normal and anomalous dispersion compensation can be taken into account, but they are usually large in size and introduce additional nonlinear accumulations; second, digital equalizers, which usually provide dispersion compensation for Wavelength-Division-Multiplexing (WDM) systems, are highly flexible and have a stable amplitude response, but are complex in design and have high costs. The last method is the fibre Bragg grating, which has the greatest advantage of wavelength coding characteristics and tunability, but it requires relatively high process accuracy. Although the above three methods can obtain large dispersion values and better dispersion compensation effects, but for the integrated on-chip photonic system, it is more desirable to have an integrated dispersion compensation scheme to adapt to the integration needs of the on-chip system.Recently, lithium niobate has received much attention due to its high quality material properties. Its ultra-wide transmission band, excellent electro-optic coefficient and second-order nonlinear coefficient compared to other materials make it possible to realize active and passive devices with various functions. As the research on thin-film lithium niobate intensifies, soliton lasers and pulse compression on lithium niobate materials have also been studied more extensively, and dispersion compensation based on thin-film lithium niobate becomes particularly important. In this paper, we explore the application of chirped Bragg gratings for dispersion compensation on the lithium niobate platform, focusing on four critical properties: central wavelength, reflectance spectrum bandwidth, Group Delay Dispersion (GDD), and group delay ripple. Initially, we simulate unapodized chirped Bragg gratings, observing significant group delay ripple due to abrupt changes in the grating envelope. To address this issue, we investigate apodized chirped gratings, which gradually modulate the effective index along the etching depth. Parameters including waveguide initial and ending width (W_b & W_e), etching depth, grating initial and ending period, grating number, apodization ratio, and gaussian parameter are systematically scanned. We simulate symmetric linear apodization, asymmetric linear apodization, and gaussian apodization functions, selecting the former two to maintain linearity of the group delay spectrum since the linear apodization function yields a linear chirp, which will not influence the linearity of group delay spectrum. Gaussian apodization offers benefits such as a smooth spectral profile and mild ripple suppression. Simulation results indicate that when waveguide initial width and waveguide ending width are both equal to 1 μm, asymmetric linear apodization yields significant group delay dispersion (0.75 ps/nm) with a corresponding group delay ripple of 0.26 ps at the expense of bandwidth (9 nm). For the other two apodization functions, optimal group delay spectra are achieved with W_b=1 μm and W_e=1.2 μm, yielding GDDs of 0.21 ps/nm and 0.19 ps/nm, respectively, with a ripple of 0.21 ps. Furthermore, simulations demonstrate improved results with an etching depth of 0.3~0.4 μm, indicating enhanced ripple suppression with larger apodization ratios, albeit with decreased bandwidth. Following simulation, we fabricate apodized chirped gratings based on these simulations, opting for the gaussian apodization function. Experimental results show a 3 dB bandwidth of 21.2 nm, slightly lower than the simulated value (41.8 nm), with a delay dispersion of 0.138 5 ps/nm, closely aligning with the simulated value (0.136 9 ps/nm). Discrepancies in measured reflectance spectrum attributes to fabrication errors, impacting bandwidth, ripple, and suppression ratio. In conclusion, this paper investigates the apodized chirped grating based on thin-film lithium niobate, analyses the influence of each parameter of apodized chirped grating on four key attributes, and summarizes the optimal selection range of the individual parameters as well as the trade-off relationship. This work lays a research foundation for the dispersion compensation technology based on thin-film lithium niobate.