This paper presents an approach to automatic verification of asynchronous round-based consensus algorithms. We use model checking, a widely practiced verification method; but its application to asynchronous distributed algorithms is difficult because the state space of these algorithms is often infinite. The proposed approach addresses this difficulty by reducing the verification problem to small model checking problems that involve only single phases of algorithm execution. Because a phase consists of a finite number of rounds, bounded model checking, a technique using satisfiability solving, can be effectively used to solve these problems. The proposed approach allows us to model check some consensus algorithms up to around 10 processes.