A novel log-polar image sensor based on non-uniform lens array was proposed in this paper. Non-uniform sampling and log-polar mapping were testified by building mathematic model. The validity of the model was verified by some design examples. Meanwhile, some key parameters were analyzed and simulated, including blank spot radius (r0), growth coefficient (q) and fill factor (ηf). Several conclusions can be obtained from the simulation. r0 decreases with M on the condition that N is unchanged and increases with N on the condition that M is unchanged. Meanwhile, ηf increases with N and tends to π/4 if N≥40. So, appropriate growth coefficient (q=1.106) was obtained on the condition that N=40. The results from the simulation support theoretical foundation for realizing log-polar transformation of based on non-uniform lens array and useful to design a novel log-polar image sensor.