We propose a high sensitivity sensor based on a mode number-encoded multi-longitudinal mode fiber laser. The fiber laser incorporates a uniform fiber Bragg grating (FBG) and a fiber Fabry-Perot interferometer (FFPI) as sensitive components in the cavity. The sensor counts the number of longitudinal modes (NLM) of fiber laser, which is caused by the mismatch between the reflection band of FBG and the transmission band of FFPI resulting from the application of external perturbation to the FBG. An electrical spectrum analyzer is adopted to analyze the NLM. The strain sensor is experimentally demonstrated to have sensitivity of as high as 0.02 \mu \varepsilon/mode.