We study neutrino physics in a model with one large extra dimension. We assume the existence of two four-dimensional branes in the five-dimensional space-time, one for the ordinary particles and the other one for mirror particles, and we investigate neutrino masses and mixings in this scheme. Comparison of experimental neutrino data with the predictions of the model leads to various restrictions on the parameters of the model. For instance, the size of the extra dimension, R, turns out to be bounded from below. Cosmological considerations seem to favor a large R. The usual mixing schemes proposed as solutions to the solar and atmospheric neutrino anomalies are compatible with our model.