We propose a new cellular network model that captures both strong repulsion and randomness between base stations. The base stations are modeled by superposition of a random shifted grid with intensity λg for the grid base stations and an independent Poisson point process with intensity λρ for the random base stations. Assuming that the typical user is associated with the base station that provides the strongest average receive signal power, we derive the association probability of the typical user. In Rayleigh fading channels, the coverage probability of the typical user at the origin is derived.