The paper introduces a new objective method for speech quality assessment called Fourier-lapped multilayer perceptron (FLMLP). This method uses an overcomplete transform based on the discrete Fourier transform (DFT) and modulated lapped transform (MLT). This transform generates the DFT and the MLT speech spectral domains from which several relevant perceptual parameters are extracted. The proposed method also employs a multilayer perceptron neural network trained by a modified version of the scaled conjugated gradient method. This neural network maps the perceptual parameters into a subjective score. The numerical results show that FLMLP is an effective alternative to previous methods. As a result, it is worth stating that the techniques here described may be potentially useful to other researches facing the same kind of problem.