In this paper, a model called Non-uniform Finite Cellular Automata (CA) Network is introduced, and its classification and computation power studied. The suggested model is similar to the original Cellular Automata Network model, with its local neighborhood property, but neighborhood deflnitions of cells are not the same (non-uniform) for each cell and determined by an algorithm. The model is similar to the Neural Network (model with its different Iocal cell (neuron) transition function definitions and with its training (or feature extraction) mode. Depending on the nature of input-output templates, computation can be done on the system. Necessary and sufficient conditions for doing computation on this model are based on the work of Tchuente, and will be elaborated upon in this paper.