Heterologous splicing is a typical tampering behavior for digital voice. It mainly uses the audio editing software to splice the voice clips recorded in different scenes, so as to achieve the purpose of changing the semantics of voice. Considering the difference of background noise in different scenes, a tampering detection algorithm based on noise consistency for digital voice heterologous splicing was proposed. Firstly, the Time-Recursive Averaging (TRA) algorithm was applied to extract the background noise contained in the voice to be detected. Then, the Change-Point Detection (CPD) algorithm was used to detect whether abrupt changes existed in the noise variance, which was used to determine whether the voice was tampered, and to locate the tampering position of the testing voice. The experimental results show that the proposed algorithm can achieve good performance in detecting the tampering position of heterologous splicing for digital voice.