Shaped charge jet has been widely applied in the military and energy sources' extraction fields; while the related investigations on the shaped charge jet penetration into concrete-like target are still limited, a series of numerical simulation works are conducted in this article. Holmquist-Johnson-Cook and Johnson-Cook models are used to describe the concrete-like targets and metal liner/casing of the shaped charge, respectively. The whole process including the formation, elongation in the air, and penetration into concretelike target of shaped charge jet is reproduced using the multi-material arbitrary Lagrange-Euler algorithm and fluid-structure interaction method implemented in LS-DYNA. Simultaneously, the striking velocities of the jet (both tip and tail) and the damage of target (diameter and depth of penetration borehole) are derived. The above constitutive models, the corresponding material parameters, and the finite element algorithms are validated by comparing with the available tests' data. The analyses of parametric influences are further performed. It indicates that for the unfragmented shaped charge jet, the penetration depth increases and the average penetration borehole diameter decreases with the standoff distance increasing, respectively; the compressive strength of concrete target has slight influence on the penetration depth of shaped charge jet; the diameter of shaped charge jet penetration borehole with aluminum liner is larger, while that with copper liner has a deeper penetration depth. It can also be found that the influence of explosive type on the penetration performance of shaped charge jet is negligible at small standoff distance, while the explosive LX-14 performs better than explosives Octol, B, and 8701 at larger standoff distance.