We show for the first time that standard model checking allows one to completely verify asynchronous algorithms for solving consensus, a fundamental problem in fault-tolerant distributed computing. Model checking is a powerful verification methodology based on state exploration. However it has rarely been applied to consensus algorithms, because these algorithms induce huge, often infinite state spaces. Here we focus on consensus algorithms based on the Heard-Of model (HO model, for short), a new computation model for distributed computing. By making use of the high abstraction level provided by this computation model, we develop a methodology for verifying consensus algorithms in every possible state by model checking. This paper describes the proposed verification methodology and the results of applying it to various consensus algorithms.