In this letter, we propose a new approach to speech enhancement based on a complex Laplacian probability density function (pdf). With a use of a goodness-of-fit (GOF) test, we discover that the complex Laplacian pdf is more desirable to describe noisy speech distribution than the conventional Gaussian pdf for speech enhancement. The likelihood ratio (LR) is computed and then applied to computation of the speech absence probability in the speech enhancement algorithm. Our evaluation shows that the proposed complex Laplacian pdf scheme provides further speech quality enhancement compared with the conventional method through a number of objective tests.