The early afterdepolarization (EAP) behavior is introduced into the Greeberg-Hasting model of discrete excitable medium through considering that some of the refractory states can be excited. The effect of the EAP on spiral wave is studied. The numerical results show that the EAP has significant influences on spiral waves when the related parameters are suitably chosen. These influences include that the EAP causes spiral wave drifting and meandering,and spiral breakup. The pattern of spiral wave is distorted. The spiral wave varies alternately between those with thick and thin arms. The period of spiral wave alters alternately between two values. The EAP induces the transition from stable spiral wave to breathing spiral wave or antispiral wave. When the excitation threshold of refractory states is very high,the EAP has no affect on the spiral wave. The EAP induced phenomena are briefly discussed.