Based on analytic soliton solutions of nonlinear coupled-mode equations (NLCME) in a uniform fiber Bragg grating (FBG), the existence of slow grating soliton (GS) is discussed. By introducing non-relativistic, adiabatic and quantum approximation to NLCMEs in the FBG with hyperbolic tangent apodization, and assuming the soliton as a particle with low velocity and invariant energy, the track equation of soliton is obtained. Numerical simulations of velocity and displacement of reflected soliton, slow soliton and standing soliton are carried out to analyze the controllable velocity characteristic of the GS. Results show that time delay of 2000 ns can occur in an apodized FBG with length of 50 meters and corresponding average velocity is 0.1 c/n. The influences of grating parameters and velocity and displacement of initial input pulse solitons on time delay are further discussed. By choosing proper parameters of the apodized FBG and the initial soliton pulse, GS with any velocity between 0 and c/n can be achieved, which facilitates the compact soliton-based optical Buffer.