We demonstrate a temperature-insensitive fiber-delay-line-stabilized (FDL-stabilized) laser based on a dual Mach-Zehnder interferometer (MZI) by using polarization maintaining fibers (PMFs). Two orthogonal polarization components of a beam are simultaneously transmitted in the interferometer. Each polarization component exhibits a unique phase shift in response to the changes in temperature, forming a dual MZI. One of the heterodyne signals is used to lock the laser frequency, while the other one is used to compensate the frequency change induced by the temperature fluctuation. The experiment shows that the laser frequency fluctuation has been suppressed at least 25 times. This is an effective method to reduce the laser frequency noise induced by the temperature fluctuation of the FDL. In this way, a compact system with less thermal shields can be realized, and the thermal equilibrium time could be decreased dramatically.