Being reversible, the watermarking information embedded in audio signals can be extracted while the original audio data can achieve lossless recovery. Currently, the few reversible audio watermarking algorithms are confronted with following problems: relatively low SNR (signal-to-noise) of embedded audio; a large amount of auxiliary embedded location information; and the absence of accurate capacity control capability. In this paper, we present a novel reversible audio watermarking scheme based on improved prediction error expansion and histogram shifting. First, we use differential evolution algorithm to optimize prediction coefficients and then apply prediction error expansion to output stego data. Second, in order to reduce location map bits length, we introduced histogram shifting scheme. Meanwhile, the prediction error modification threshold according to a given embedding capacity can be computed by our proposed scheme. Experiments show that this algorithm improves the SNR of embedded audio signals and embedding capacity, drastically reduces location map bits length, and enhances capacity control capability.