Different methods for Blind Source Separation (BSS) have been recently proposed. Most of these methods are suitable for separating either a mixture of sub-Gaussian source or a mixture of super-Gaussian sources. In this paper, a unified statistical approach for separating the mixture of sub-Gaussian and super-Gaussian source is proposed. Source separation techniques use an objective function to be optimized. The optimization process requires probability density function to be expressed in the terms of the random variable. Two different density models have been used for representing sub-Gaussian and super-Gaussian sources. Optimization of the objective function yields different nonlinear functions. Kurtosis has been ušed as measure of Gaussianity of a source. Depending upon the sign of kurtosis one of the nonlinearities is ušed in the proposed algorithm. Simulations with artificiaily generated as well as audio signals demonstrate effectiveness of the proposed approach.