Mutators, cells with elevated mutation rates, are common in both natural microbial populations and in human cancers. Recent experiments have shown that mutators can invade a population, but the invasion dynamics and probability couldn’t be explained by mutation rates alone. Here we show, analytically and in simulation, that mutation bias (which types of mutations are likely to occur) can play an important role in the emergence of mutators. A mutator that reduces or reverses the historically prevailing mutational bias is shown to have an increased chance of invasion, while chances are reduced when the bias is reinforced. These findings are important when trying to understand natural populations or competition experiments with mutators.