This algorithm is a extremely fast algorithm for sigma selection of Gaussian RBF kernel in the scenarios of classification models. The Gaussian radial basis function (RBF) is a widely used kernel function in support vector machine (SVM). The kernel parameter σ is crucial to maintain high performance of the Gaussian SVM. Most previous studies on this topic are based on optimization search algorithms that result in large computation load. In this paper, we propose an analytical algorithm to determine the optimal σ with the principle of maximizing between-class separability and minimizing within-class separability. An attractive advantage of the proposed algorithm is that no optimization search process is required, and thus the selection process is less complex and more computationally efficient. Experimental results on seventeen real-world datasets demonstrate that the proposed algorithm is fast and robust when using it for the Gaussian SVM.