An adaptive network is a kind of co-evolutionary network in which the behaviors of nodes and the dynamics of the network affect each other. A susceptible-infected-susceptible epidemics spreading model in the adaptive network is proposed using cellular automata. Under different rewriting rules for avoiding the epidemic spreading, the changes in epidemic dynamics and the properties of the network statistic are investigated. The simulation results show that the introduction of rewiring can slow down the spreading speed of epidemic and suppress the infected scale of epidemic. The random rewiring rules make the properties of an original network with any topology tend to those of a random network. Furthermore, the proposed cellular automata model can clearly exhibit the phenomenon of bi-stability in epidemic dynamics.