A crystal plasticity model considering the hydrostatic pressure dependence is presented and validated using several numerical examples. Some metallic materials clearly show higher flow stress under uniaxial compression than that under uniaxial tension, and this phenomenon is called the strength-differential (S-D) effect. Since the S-D effect often occurs in iron-based materials, the understanding and modeling of its mechanical characteristics is important in industrial and engineering fields. The S-D effect may result from the hydrostatic pressure dependence of plastic deformation. Therefore, in this study, a crystal plasticity model is modified to account for this dependence. The proposed model is combined with the homogenization-based finite element method. This model adequately reproduces the S-D effect observed experimentally, thus its advantages over the previously introduced Taylor polycrystalline model, which overestimates the flow stress and fails to represent the strong inhomogeneity of hydrostatic pressure distribution at a crystalline scale, is highlighted. In addition, initial and subsequent plastic work contours are evaluated and a forming limit diagram is analyzed to characterize the new model.