The propagation of light waves in quasi-periodic photonic crystals based on the Thue-Morse sequence is investigated by the transfer matrix method. The linear transmission spectrum of such photonic structures exhibits a fractal nature of self-similar pattern, so as the electric field distribution. If the order number of Thue-Morse sequence is odd, the electric-field profile in the quasicrystal is asymmetric. In the case of Kerr nonlinearity, this will result in different bistability sensitive to the propagation direction. Under a certain condition, the light wave can unidirectionally transmit with external pump-assisting. This provides the realization of all-optical diode.