In an intermediate feed rate regime of Gray-Scott model, the dominant instability will change from profile instability into drift instability with the increasing feed rate. In this case, the spike location begins to oscillate when the system is first destabilized by the drift instability. Our work is focused on the dynamics of spike location. Basically, we derive a coupled ODE-PDE system to describe the motion using the boundary layer theory. The numerical simulations agree with analytical results on the critical bifurcation value. This ODE-PDE formulation of dynamics of pulse can be extended and implemented in other reaction-diffusion systems.