In this paper, we investigate methods to enhance the perceptual quality of MP3-coded audios. Based on the high frequency reconstruction method by Liu, in the proposed method, we determine adaptively the starting point of high frequency reconstruction. We also present an improved linear estimation method. For high frequency component generation, we compare two methods. One is a replication of low-frequency components and the other is an insertion of additive white Gaussian noise signals. Through subjective tests, we shall show that the proposed method can improve the perceptual quality of MP3-coded audio.