Fiber Fabry-Perot tunable filter (FFP-TF) is one of the core components of the fiber Bragg grating sensor demodulation system. Its stability is very important to the demodulation accuracy, and the temperature drift is the influence one of the key factors of its stability. The nonlinear mapping ability of the least squares support vector machine (LSSVM) can effectively compensate for drift. In this paper, aiming at the problem that the traditional LSSVM model parameter selection is easy to fall into the local optimum, based on the improved beetle search particle swarm optimization algorithm to find the optimal penalty factor and kernel parameters of the LSSVM model in the global scope. The experimental results show that using the optimized LSSVM to compensate the temperature drift of FFP-TF can reduce the temperature drift error from the maximum amplitude of 1025.21 pm to ±3.03 pm, and improve the temperature stability of FFP-TF demodulation in a variable temperature environment.