A physical and mathematical model is presented to explain processivity of proteins on DNA. In this model, a DNA-targeting protein such as a restriction enzyme can diffuse to the DNA surface and nonspecifically bind to it. Once on the DNA surface it will either move along the DNA or equilibrate with the surrounding region. Owing to the nonspecific binding, the search for a specific site on the DNA occurs in a reduced dimensionality, and the protein appears processive when moving from one specific site to another. The simplest version of this nonspecific-binding-facilitated diffusion model is solved and the results quantitatively explain experimentally observed dependence of the processivity ratio on the intervening DNA length between two specific sites.