Abstract: Conduction velocity (CV) restitution and action potential duration (APD) restitution caused by relative refractory state of excitable medium and their effects on the evolution behavior of spiral waves are investigated with cellular automata model. The numerical simulation results showed that when the excitability of the excitable medium is low, the cell in the relative refractory state cannot be excited, the slope of the CV restitution curve is close to zero and the slope of the APD restitution curve is zero, so the spiral wave pattern can maintain continuity and thus rotate stably or meander; when the excitability of the excitable medium is high, the cell in the relative refractory state can be excited, the slopes of the CV restitution curve and APD restitution curve are non-zero, and the degree of the breakup of spiral wave is qualitatively proportional to the steepness of the CV restitution curve, while the fact that the maximum slope of the APD restitution curve is greater than 1 accounts for the multiple-spiral waves originated from spiral wave. The numerical simulation results also showed that the CV restitution is positively correlated with the APD restitution, and this conclusion is consistent with the experimental results. The results in this paper can provide a reference for understanding the mechanism of the evolutionary behavior of spiral waves in excitable medium.