The effects of axial strain on beating frequency from a short cavity polarization-maintaining erbium-doped fiber (PM-EDF) based distributed Bragg reflector (DBR) laser were investigated theoretically and experimentally for the first time. This type of single-mode DBR fiber laser based ultrasensitive sensor has been extensively developed for measuring kinds of measurands, but the cross-sensitivity of axial strain was usually ignored. A DBR fiber laser with an effective cavity length of $sim$1 cm formed by a pair of FBGs written on a PM-EDF was fabricated for demonstration. This laser operated in dual-polarization single-longitudinal mode stably. The frequency of the beating signal generated by two orthogonal polarizations was found to be proportional to the axial strain applied on the cavity. A linear strain sensitivity of 0.640 $hbox{GHz/m}varepsilon$ was obtained, with a fiber birefringence of around 8.65e-5. For the fiber with larger birefringence, the sensitivity to the axial strain will be increased. So the effects of axial strain should be considered when the structure is utilized as a high-resolution sensor, especially for a polarization-maintaining system. The single-mode DBR laser made of high birefringent fibers also has a potential application in frequency tunable microwave generation.