A local oscillation laser seed source with narrow linewidth and large tuning bandwidth is one of the core components of space coherent optical communication systems. Using the narrow linewidth seed source in combination with external electro-optical modulation and narrowband grating filtering, narrow line width and high tuning bandwidth can be achieved, but the fiber Bragg grating controlled by temperature is difficult to adapt to the high-speed Doppler frequency shift between moving platforms. In this paper, a closed-loop system of a fiber Bragg grating controlled by piezoelectric ceramics in combination with the gradient descent algorithm is used to realize the relative locking of the fiber grating and the injected laser wavelength. The proposed scheme can adapt to spatial Doppler shift above 40 MHz/s.