This paper proposes a voice activity detector (VAD) based on the complex Laplacian model. With the use of a goodness-of-fit (GOF) test, it is discovered that the Laplacian model is more suitable to describe noisy speech distribution than the conventional Gaussian model. The likelihood ratio (LR) based on the Laplacian model is computed and then applied to the VAD operation. According to the experimental results, we can find that the Laplacian statistical model is more suitable for the VAD algorithm compared to the Gaussian model.