Abstract The nonreciprocal photonic spin Hall effect features the different reflected or transmitted spin shifts along two opposite incident wave propagating directions. However, previous investigations have always focused on the features of the photonic spin Hall effect along one incident wave propagating direction. How to achieve the nonreciprocal photonic spin Hall effect remains obscure. Here, we theoretically study the nonreciprocal photonic spin Hall effect in the asymmetric multilayered structure containing the Bulk Dirac Semimetal and other dielectric materials. It is found that under the horizontal polarization the maximum reflected spin shift value along one direction is up to around times of the incident wavelength at , but it is only times of the incident wavelength at along the other direction, which reflects the nonreciprocity of photonic spin Hall effect and thus can act as the photonic spin Hall diode. Such a sizeable directional difference between the reflected spin shifts along these two opposite directions originates from the fact that this structure loses its mirror symmetry and becomes an asymmetrical one, and the obvious difference in the values of the reflected spin shifts along the two directions can be attributed to the large difference in the values of . At the same time, we find that the Fermi energy of the Bulk Dirac Semimetal can effectively tune the spin shift along the backward direction, as well as the difference between the spin shifts for two different propagating directions, which causes the controllable nonreciprocal photonic spin Hall effect. Our results establish the alternative configuration for realizing the nonreciprocal photonic spin Hall effect, which facilitates the potential applications in the spin photonic devices.