An all-fiber sensing system based on the Mach-Zehnder Interferometer (MZI) and Fiber Bragg Grating (FBG) was proposed for the measurement of transverse pressure and temperature simultaneously. The MZI was fabricated by splicing of a lateral-offset Multi-Core Fiber (MCF) with two single mode fibers, the modal interference was formed due to the mode field mismatch among MCF and Single Mode Fibers (SMFs), which made the external pressure directly acted on the light field inside of the multi-core fiber, thus a high pressure sensitivity of interferometer can be achieved. Experimental results show that the pressure sensitivity of the MZI is 28.57 nm/(N·mm-1), and the linearity is 0.997, while FBG is not sensitive to the pressure change. Both the MZI and the FBG show a good linearity between the wavelength shift and temperature, and the sensitivity is 56.1pm/℃ and 11.3pm/℃, respectively. For a spectrometer with a resolution of 0.02 nm, the proposed sensor can reach a resolution of 7.0×10-4N/mm for pressure and of 0.03℃ for temperature. The transmission spectrum of the MZI and the resonance peaks of the FBG have different spectral responses to pressure and temperature changes. By using optical spectrum analyzer to monitor the wavelength shift of the transmission spectrum of the sensor, so that the dual-parameters of pressure and temperature can be measured conveniently.The proposed sensor has a simple structure a high sensitivity, it can be well applied to transverse pressure measurement.