Muon tomography is a promising method in the detection and imaging of high Z material. In general, considering the quality of track reconstruction in imaging, a detector of good position resolution, high efficiency and large area is required. This paper presents the design and study of a prototype of position sensitive MRPC with 0.15 mm narrow gas gap and 2.54 mm strip readout. Through a cosmic-ray experiment, the performance of MRPC module is carefully observed and each channel is calibrated. Through an X ray experiment with a narrow slit, the position resolution is studied. The results show that the time resolution of the module can reach 61ps and the spatial resolution can reach 0.36 mm.