A novel fiber strain sensor based on the fiber laser's transient regime is reported. A Sagnac fiber loop and a fiber Bragg grating(FBG) that also acts as the sensing element form the linear Fabry-Perot cavity, in which a long-period grating(LPG) is inserted. The original peak wavelength of the FBG, whose bandwidth is 0.23nm, is 1557.98nm and located on the left side of the LPG dip (1557.4nm). The light reflected from the Sagnac loop and the FBG is transmitted through the LPG twice in each round trip, and the transmission loss increases with the strain-induced wavelength shift of the FBG, which in turn modifies the laser build-up time. The strain value can be obtained by measuring the build-up time of the laser. In the present experiment, the sensor's sensitivity and resolution can be adjusted by simply controlling the pumping level. When the pump pulse's high level and low level are 32 and 6mW, respectively, a sensitivity of 7×10-6ε/μs and resolution of 7×10-7ε are achieved.