According to low-emittance, short-pulse and low-charge-in-single-bunch properties of laser-driven proton beam, we study the feasibility of cavity beam position monitor (BPM) to measure the transverse position of proton beam generated by laser accelerator. In view of the large transverse distribution and divergence angle of proton beam, we derive the output signal when it goes through the cavity BPM, and the result shows that the output signal is identical to that generated by the beam passing through the symmetry center of the transverse distribution and at a certain angle of inclination. Based on the above principle, we use CST software to design and simulate cavity BPM, and determine the scheme of rectangular cavity with coupling waveguide. We discuss the applicability of this scheme for laser-accelerated beam and the resolution of different laser-driven proton beam parameters, and estimate the resolution of PW laser acceleration system.