3-D numerical simulations for rupture process of a large asperity on a subduction fault are carried out in order to examine whether the whole area of an asperity always breaks at once or not during an earthquake. Our quasi-static simulation in an elastic half-space includes a rate- and state-dependent friction. We examine the effect of lateral dimension of an asperity which extends the whole seismogenic width in dip direction on the slip behavior. In cases of the asperity with comparable dimension to the seismogenic width, the whole area of the asperity can break at once and its seismic cycle shows a regular periodic behavior. However, in cases with much larger lateral dimension, the asperity does not break its whole area at once. In addition, its slip behavior becomes complex within a certain range. This suggests that the slip complexity in earthquake fault may be an intrinsic property in the system.