We present a simplified model of DNA for computer simulation of melting dynamics. This model is simple enough to allow simulation times up to the microsecond range for DNA duplexes with tens of base pairs, while its level of detail is sufficient to describe individual base pairs and individual hydrogen bond formation and breakage. We have applied this model to the simulation of the melting of two model B-DNA decamers. The DNA melting profiles are similar to those seen in experiment, as are the differences between duplexes containing only AT pairs versus those with only CG pairs.