Clutter suppression, especially in time-varying environments is a hindrance that must be solved for radar systems applied to unmanned vehicles. However, exponential moving average (EMA) method, a common background subtraction technique, does not handle such a situation very well because the fixed parameter constrains the updating of the estimated clutter. In this paper, we propose a novel adaptive clutter suppression algorithm to adjust the parameter of EMA method under the background of time-varying clutter. The main idea is to adopt a low-complexity time-averaged variable forgetting factor (TAVFF) mechanism. The proposed algorithm is assessed with data recording measured background clutter and a simulated moving target. The simulation results demonstrate our proposed algorithm has achieved both fast convergence and good steady-state performance.