We propose a novel training scheme to optimize voice conversion network with a speaker identity loss function. The training scheme not only minimizes frame-level spectral loss, but also speaker identity loss. We introduce a cycle consistency loss that constrains the converted speech to maintain the same speaker identity as reference speech at utterance level. While the proposed training scheme is applicable to any voice conversion networks, we formulate the study under the average model voice conversion framework in this paper. Experiments conducted on CMU-ARCTIC and CSTR-VCTK corpus confirm that the proposed method outperforms baseline methods in terms of speaker similarity.