Although tunable Fabry-Perot (F-P) filters are widely acknowledged as fiber Bragg grating (FBG) demodulators, F-P filters exhibit drift error when subjected to ambient temperature and piezo-electrical transducer (PZT) hysteresis. To address the drift issue, the majority of the existing literature makes use of additional devices like the F-P etalon and gas chamber. In this study, a novel drift calibration method based on two-stage decomposition and hybrid modeling is proposed. The initial drift error sequences are broken down into three frequency components using the variational mode decomposition (VMD), and the medium-frequency components are further broken down using the secondary VMD. The initial drift error sequences are significantly simplified by the two-stage VMD. On this foundation, the long short-term memory (LSTM) network and polynomial fitting (PF) are used to forecast the low-frequency and high-frequency drift errors, respectively. The LSTM enables the prediction of intricate nonlinear local behaviors, while the PF method predicts the overall trend. The benefits of LSTM and PF can be effectively utilized in this manner. Compared to the single-stage decomposition, two-stage decomposition achieves superior results. The suggested method is an affordable and effective alternative to the current drift calibration techniques.