In order to explore the feasibility of using conventional fiber to fabricate weak fiber Bragg grating (WFBG) and reduce the material cost and transmission loss, a WFBG was fabricated on a conventional single-mode fiber (CSMF) based on phase mask method. The unified optical field equation of phase mask grating system was established, and the influence of optical field distribution on center wavelength and reflectivity of FBG was analyzed. The influence of phase mask length and average change of refractive index on reflectivity and 3dB bandwidth of FBG was analyzed by transfer matrix method, which provides theoretical basis for improving WFBG lithography. WFBGs were fabricated on CSMFs by 248nm UV excimer laser. The effects of phase mask length, exposure energy, exposure frequency, and exposure times on central wavelength, reflectivity, and 3dB bandwidth of WFBG were respectively analyzed. Two kinds of WFBGs with narrow and wide bandwidths were fabricated with reflectivity and 3dB bandwidth of 0.0016 and 0.10nm, 0.00006 and 0.34nm, respectively. Theoretical and experimental results show that WFBG can be fabricated on CSMF stably by the multi-pulse exposure of UV excimer laser based on the phase mask method, which provides a reference for the material selection of the weak reflection fiber grating.