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The fixed-point algorithm and infomax algorithm are two of the most popular algorithms in independent component analysis (ICA). However, it is hard to take both stability and speed into consideration in processing functional magnetic resonance imaging (fMRI) data. In this paper, an optimization model for ICA is presented and an improved fixed-point algorithm based on the model is proposed.In the new algorithms a small step size is added to increase the stability. In order to accelerate the convergence, an improvement on Newton method is made,which makes cubic convergence for the new algorithm.Applying the algorithm and two other algorithms to invivo fMRI data, the results show that the new algorithm separates independent components stably,which has faster convergence speed and less computation than the other two algorithms. The algorithm has obvious advantage in processing fMRI signal with huge data.