Corrugated sandwich panels with outstanding load-bearing and energy absorption capacities are widely used in aerospace, naval and automobile industries. Herein, a series of modified sinusoidal corrugated (MSC) sandwich panels, with multiple layers and gradient design, are developed and fabricated by additive manufacturing. An analytical model for quasi-static compression performance was established by using Timoshenko beam and plastic hinge theory. Corresponding experiments and finite element analysis are conducted to investigate the out-of-plane compressive failure mechanism and mechanical performance. The energy absorption capability of graded MSC sandwich panels is studied to reveal the influence of gradient design. The results reveal that the proposed analytical model can accurately predict the compressive modulus and ultimate strength of multi-layer MSC sandwich panels with a maximum deviation of <25%. The introduction of gradient design decreases the initial peak strength and the undulation of load-carrying capacity during nonlinear deformation. The energy absorption ratio slightly increased due to the improved energy absorption process, which can be attributed to the controllable deformation behavior of sandwich core.