In low light condition, the signal-to-noise ratio (SNR) is low and thus the captured images are seriously degraded by noise.Since low light images contain much noise in flat and dark regions, contrast enhancement without considering noise characteristics causes serious noise amplification. In this paper, we propose low light image enhancement based on two-step noise suppression. First, we perform noise aware contrast enhancement using noise level function (NLF). NLF is used to get a noise aware histogram which prevents noise amplification, and we use the noise aware histogram in contrast enhancement. However, the increase of intensity by contrast enhancement reduces the visibility threshold, which makes noise visible by human eyes. Second, we utilize a just noticeable difference (JND) model from luminance adaptation to suppress noise based on human visual perception. Experimental results show that the proposed method successfully enhances contrast in low light images while minimizing noise amplification.