This paper presents a robust approach to improve the performance of voice activity detector (VAD) in low signal-to-noise ratio (SNR) noisy environments. To this end, we first generate sparse representations by Bregman Iteration based sparse decomposition with a learned over-complete dictionary, and derive a kind of audio feature called sparse power spectrum from the sparse representations. we then propose a method to calculate the short segment average spectrum and long segment average spectrum from sparse power spectrum. Finally, we design a criterion to detect speech region and non-speech region based on the above average spectrum. Experiments show that the proposed approach further improves the performance of VAD in low SNR noisy environments.