Abstract: Taking normal functions as membership functions of fuzzy variables the approaching error of a fuzzy neural network to a group of samples is denoted as the sum of two nonnegative functions of two independent and adjustable groups of parameters that can be trained one after another. One of the two parameter groups can be obtained directly by taking its corresponding nonnegative functions to be zero and another parameter group can be obtained through learning according to its corresponding nonnegative functions--performance index. Based on the analysis of the performance index a new algorithm, two-stage random search algorithm with variable radius, is put forward. Some examples show that the algorithm is simple and convenient and can make fuzzy neural network attain high precision.