Using numerical methods, we study pulse propagation near the band edge of a one-dimensional photonic band gap material with a spatial gradiation in the linear refractive index, together with a nonlinear medium response. We find that such a structure can result in unidirectional pulse propagation. That is, the field will be transmitted for, say, a left-to-right direction of propagation, while for right-to-left nearly complete reflection occurs. This behavior constitutes the operational mechanism for a passive optical diode.