Gaussian mixture model （GMM） is a classic probability model， which is usually used in the field of unsupervised learning to determine the class distribution of unlabeled samples. As an important method for solving GMM parameters， the expectation-maximization （EM） algorithm determines the parameters and component coefficients by calculating the optimal solution of the GMM likelihood function. The use of EM algorithm to solve GMM has the following two defects： EM algorithm is prone to getting stuck in a local optimal solution， and the relevant parameters of the GMM basic model determined by the EM algorithm are unstable， especially for high-dimensional data. For this reason， this paper proposes a GMM solution method based on statistical-aware （SA） strategy， i.e. SA-GMM method. Starting from the estimation of the unknown probability density function of a given data set， the method establishes the correlation between kernel density estimation （KDE） technology and GMM. To avoid the selection of KDE’s over-smoothing bandwidth， the goal is to simultaneously minimize the empirical risk between KDE and GMM and the structural risk of KDE’s bandwidth. The experiments on 11 standard probability distributions confirm the feasibility， rationality， and effectiveness of SA-GMM. And it is also shown that the proposed SA-GMM method can obtain the better performance on probability density function estimation than EM-based GMM and its variant.