Numerous attempts have been made to obtain earthquake statistics from a theoretical-physics perspective, but these studies mostly involve regular earthquakes. In recent years, a new category of earthquakes, referred to as slow earthquakes, has been discovered. Slow earthquakes emit only weak or no seismic signals and have different statistics than regular earthquakes. Here we propose a physical model for the tremor, which is a type of slow earthquake, introducing two competing timescales in a cellular automaton model. The proposed model reproduces some observation results for tremors, such as enduring events, moment-duration scaling, size distribution, and the power spectrum of the moment rate function.