The stability of the Bianchi type I anisotropic brane cosmology is analyzed in this paper. We also study the effects of the brane solution by comparing the models on the 3-brane and the models in the conventional Einstein space. The analysis is presented for two different models: one with a perfect fluid and the other with a dilaton field. It is shown that the anisotropic expansion is smeared out dynamically for both theories in the large time limit, independent of the models of different types of matter. The initial states are, however, dramatically different. A primordial anisotropic expansion will grow for the conventional Einstein's theory. On the other hand, it is shown that the initial state is highly isotropic for the brane universe, except for a very particular case. Moreover, it is also shown that the Bianchi type I anisotropic cosmology is stable against any anisotropic perturbation for both theories in the large time limit.