To explore the physical mechanism of sweeping nonlinearity of a Fabry-Perot(F-P) tunable filter based on a PZT and to obtain the optimized scheme for the characteristics of linear wavelength sweeping, a wavelength-swept laser based on the F-P tunable filter was developed. The transmission time domain method was used to research the output nonlinearity of the wavelength-swept laser and the changed sweeping nonlinear characteristics in different sweeping frequencies were obtained. Then, it points out the change is caused by capacitive load characteristics of the PZT from the actuator in the tunable filter. With spectroscopy, the relationship among dynamical sweeping nonlinearity, sweeping range and driving frequency was obtained and it is in good agreement with that of the theoretical analysis. Finally, a new drive scheme based on a voltage follower was proposed to optimize the characteristics of linear wavelength sweeping. The experimental results show that this method promotes the linear responsibility of high-speed wavelength-sweeping. The scheme is applied in FBG interrogation system and obtained demodulation nonlinearity is 0 998 44 at a wavelength-swept speed of 1 000 Hz.