Cancer is a complex disease involving multiple genomic alterations that disrupt the dynamic response of signaling networks. The heterogeneous nature of cancer, which results in highly variable drug response, is a major obstacle to developing effective cancer therapy. Previous studies of cancer therapeutic response mostly focus on static analysis of genome-wide alterations, thus they are unable to unravel the dynamic, network-specific origin of variation. Here we present a network dynamics-based approach to integrate cancer genomics with dynamics of biological network for drug response prediction and design of drug combination. We select the p53 network as an example and analyze its cancer-specific state transition dynamics under distinct anticancer drug treatments by attractor landscape analysis. Our results not only enable stratification of cancer into distinct drug response groups, but also reveal network-specific drug targets that maximize p53 network-mediated cell death, providing a basis to design combinatorial therapeutic strategies for distinct cancer genomic subtypes.