This study aimed to evaluate the performance of sandwich panels with graded foam cores of layered densities against combined blast and fragment impact loading, and to ascertain the optimal gradient of core configuration that would maximize the performance of sandwich panels against combined loading. First, based on a recently developed composite projectile, impact tests of the sandwich panels against simulated combined loading were conducted to provide a benchmark for the computational model. Second, a computational model, based on three-dimensional finite element simulation, was constructed and verified by means of a comparison of the numerically calculated and experimentally measured peak deflections of the back facesheet and the residual velocity of the penetrated fragment. Third, the structural response and energy absorption characteristics were examined, based on numerical simulations. Finally, the optimal gradient of core configuration was explored and numerically examined. The results indicated that the sandwich panel responded in a combined manner involving global deflection, local perforation and perforation hole enlargement. As the impact velocity increased, both the peak deflection of the back facesheet and the residual velocity of the penetrated fragment increased. The front facesheet was found to be the most important sandwich component in consuming the kinetic energy of the combined loading. Thus, the compaction of the foam core would be facilitated by placing the low-density foam at the front side. This would further provide a larger deflecting space for the front facesheet, thus reducing the deflection of the back facesheet. The gradient of core configuration was found to have limited influence on the anti-perforation ability of the sandwich panel. Parametric study indicated that the optimal gradient of foam core configuration was not sensitive to time delay between blast loading and fragment impact loading, but was sensitive to the asymmetrical facesheet of the sandwich panel.