The tumor suppressor protein p53 can lose its function upon DNA-contact mutations (R273C and R273H) in the core DNA-binding domain. The activity can be restored by second-site suppressor or rescue mutations (R273C_T284R, R273H_T284R, and R273H_S240R). In this paper, we elucidate the structural and functional consequence of p53 proteins upon DNA-contact mutations and rescue mutations and the underlying mechanisms at the atomic level by means of molecular dynamics simulations. Furthermore, we also apply the docking approach to investigate the binding phenomena between the p53 protein and DNA upon DNA-contact mutations and rescue mutations. This study clearly illustrates that, due to DNA-contact mutants, the p53 structure loses its stability and becomes more rigid than the native protein. This structural loss might affect the p53-DNA interaction and leads to inhibition of the cancer suppression. Rescue mutants (R273C_T284R, R273H_T284R and R273H_S240R) can restore the functional activity of the p53 protein upon DNA-contact mutations and show a good interaction between the p53 protein and a DNA molecule, which may lead to reactivate the cancer suppression function. Understanding the effects of p53 cancer and rescue mutations at the molecular level will be helpful for designing drugs for p53 associated cancer diseases. These drugs should be designed so that they can help to inhibit the abnormal function of the p53 protein and to reactivate the p53 function (cell apoptosis) to treat human cancer.