The photonic spin Hall effect (SHE) manifests itself as the spin-dependent splitting of light beam. Usually, it shows a symmetric spin-dependent splitting, i.e., the left- and right-handed circularly polarized components are equally separated in position and intensity for linear polarization incidence. In this paper, we theoretically propose an asymmetric spin-dependent splitting at an air-glass interface under the illumination of elliptical polarization beam and experimentally demonstrate it with the weak measurement method. The left- and right-handed circularly polarized components show expectedly unequal intensity distributions and unexpectedly different spin-dependent shifts. Remarkably, the asymmetric spin-dependent splitting can be modulated by adjusting the handedness of incident polarization. The inherent physics behind this interesting phenomenon is attributed to the additional spatial Imbert-Fedorov shift. These findings offer us potential methods for developing new spin-based nanophotonic applications.