This study investigated the dynamic response of continuous-density-graded aluminum foam sandwich tubes subjected to internal explosion loads. A finite element model for continuous-density-graded aluminum foam and sandwich tubes was established in polar coordinates using 3D-Voronoi technology. The influences of core density distributions, such as positive-gradient, negative-gradient, and V-shaped gradient including middle-high-gradient (high in the middle and low at both ends) and middle-low-gradient (low in the middle and high at both ends), core density gradient, assembly methods of tube walls and the core, and the length-to-diameter ratio of explosives on the anti-shock performance of the sandwich tube structure were analyzed. Results demonstrate that, for the same core density gradient, the maximum deformation of the outer tube in the sandwich tube with a negative-gradient core is the least, while the sandwich tube with a middle-low-gradient core exhibits the highest specific energy absorption, and the sandwich tube with a middle-high-gradient core shows the weakest anti-shock performance. As core density gradient increases, the maximum deformation of the outer tube in the sandwich tube with a negative-gradient core significantly decreases. The specific energy absorption for the sandwich tube with a middle-low-gradient core rises initially before declining, while the anti-explosion performance of the sandwich tube with a middle-high-gradient core deteriorates. Optimal bonding between tube walls and the core effectively improves the specific energy absorption of sandwich tubes with a uniform, negative-gradient, or middle-low-gradient core, but it also increases the maximum deformation of the outer tube. For varying length-to-diameter ratios of explosives, the maximum deformation of the outer tube in the sandwich tube with a negative-gradient core is smaller. The present work aims to provide valuable insights for designing such structures for protective engineering applications.