A widely used contrast enhancement method, the histogram equalization (HE) often produces images with unnatural appearances and visually disturbing artifacts because the HE compels the enhanced image to follow the uniform distribution. An adaptive histogram equalization using logarithmic mapping is presented, with a proposed algorithm based on a bin underflow and overflow method that achieves contrast enhancement by putting constraints on each histogram component differently. To incorporate characteristics of the human visual system, the logarithmic mapping function is used as constraint function, while the rate of contrast enhancement is controlled by determining the control parameters with the characteristics of the original image. The experimental results show that the proposed algorithm not only keeps the original histogram shape features, but also enhances the contrast effectively. Due to its simplicity, the proposed algorithm can be applied by simple hardware and processed in a real-time system.