This paper proposes an efficient separation method of the composite images by using independent component analysis(ICA) based on neural networks of the approximate learning algorithm. The Proposed learning algorithm is the fixed point(FP) algorithm based on Secant method which can be approximately computed by only the values of function for estimating the root of objective function for optimizing entropy. The secant method is an alternative of the Newton method which is essential to differentiate the function for estimating the root. It can achieve a superior property of the FP algorithm for ICA due to simplify the composite computation of differential process. The proposed algorithm has been applied to the composite signals and image generated by random mixing matrix in the 4 signal of 500-sample and the 10 images of $512{ imes}512-pixel$, respectively The simulation results show that the proposed algorithm has better performance of the learning speed and the separation than those using the conventional algorithm based method. It also solved the training performances depending on initial points setting and the nonrealistic learning time for separating the large size image by using the conventional algorithm.