A novel fiber-laser-based strain sensor is proposed and experimentally demonstrated. The laser cavity is composed of a high-birefringence Sagnac fiber loop mirror (HiBi-SFLM) and a fiber Bragg grating (FBG) which also acts as a strain-sensing element. In the linear region of the HiBi-SFLM reflection spectrum, when the strain applied on the FBG makes the Bragg grating wavelength shift, the laser output power changes due to reflectivity variation of the HiBi-SFLM. Experimental results show that the laser output power varies almost linearly with the applied strain. The measurement of the output power can be performed by a conventional photo-detector.