In this paper, multi-channel allocation in wireless sensor and actuator networks is formulated as an optimization problem which is NP-hard. In order to efficiently solve this problem, a distributed game based channel allocation (GBCA) Algorithm is proposed by taking into account both network topology and routing information. For both tree/forest routing and non-tree/forest routing scenarios, it is proved that there exists at least one Nash Equilibrium for the problem. Furthermore, the sub-optimality of Nash Equilibrium and the convergence of the Best Response dynamics are also analyzed. Simulation results demonstrate that GBCA significantly reduces the interference and dramatically improves the network performance in terms of delivery ratio, throughput, channel access delay, and energy consumption.