The traditional Hash functions use a chain-like structure, which can not make best use of the 2D property of graphics or images. The chain-like structure is low in efficiency when implemented on a parallel computing platform. A new structure of Hash function is proposed to overcome these shortcomings and the time complexity is as low as o(logn) on a parallel computing platform. Some fundamental problems regarding the structure are analyzed. With this structure, a Hash function based on cellular neural network is proposed, which shows satisfactory randomness sensitivity to input and resistance to collision with simulation experiments.