This paper proposes a Voice Conversion (VC) method from Tibetan Amdo dialect to Tibetan U-tsang dialect based on Generative Adversarial Networks (GANs). An inevitable problem with the traditional VC framework is that the acoustic feature vector output from the conversion model is over-smoothing, which leads to a drop in the quality of the converted speech. This is because in the training phase of acoustic model, a specific probability model is used to model the distribution of data, so that the output of a relatively average parameter of the model is considered to be optimal. Acoustic parameter over-smoothing occurs as long as the analytical form of the model distribution is artificially designed. In order to overcome this problem, the VC framework proposed in this paper uses GANs as the modeling network of the acoustic model, directly uses a generator model to learn the distribution of data, and guides the generator through a discriminator model. The training of the model makes the sample distribution of the model close to the distribution of the target speaker data samples, thus alleviating the problem of over-smoothing of the converted speech spectrum. The experimental results show that the proposed method is superior to VC based on Deep Neural Networks (DNNs) in the sound quality and similarity of the converted speech.