This paper proposes audio coding using an efficient long-term prediction method to enhance the perceptual quality of audio codecs to speech input signals at low bit-rates. The MPEG-4 AAC-LTP exploited a similar concept, but its improvement was not significant because of small prediction gain due to long prediction lags and aliased components caused by the transformation with a time-domain aliasing cancelation (TDAC) technique. The proposed algorithm increases the prediction gain by employing a deharmonizing predictor and a long-term compensation filter. The look-back memory elements are first constructed by applying the de-harmonizing predictor to the input signal, then the prediction residual is encoded and decoded by transform audio coding. Finally, the long-term compensation filter is applied to the updated look-back memory of the decoded prediction residual to obtain synthesized signals. Experimental results show that the proposed algorithm has much lower spectral distortion and higher perceptual quality than conventional approaches especially for harmonic signals, such as voiced speech.