This paper proposes a Mel-Wiener filter to enhance Mel-LPC spectra in the presence of additive noise. The transfer function of the proposed filter is defined by using a first-order all-pass filter instead of unit delay. The filter coefficients are estimated based on minimization of the sum of the square error on the linear frequency scale without applying the bilinear transformation and efficiently implemented in the autocorrelation domain. The proposed filter does not require any time-frequency conversion, which saves a large amount of computational load. The performance of the proposed system is comparable to that of ETSI AFE. The optimum filter order is found to be 3, and thus filtering is computationally inexpensive. The computational cost of the proposed system except VAD is 53% of ETSI AFE.