The denoising of interferometric phase images attracts many researchers. Natural image denoising algorithms based on neural networks are often proposed in the development of deep learning methods. A neural network, In-CNN, is derived from an advanced natural image denoising network and proposed for interferometric phase image denoising. Preactivation and residual learning methods are combined and applied to the function of the neural network nodes. Considering the particularity of the interferometric phase image, we propose a neural network based on the rational application of the preactivation mode and feedforward mapping, which is different from previous natural image denoising networks. We also construct a training set for an interferometric phase image denoising neural network. We experimentally verify that our model performs better than state-of-the-art interferometric phase image denoising methods based on sparse representation and advanced natural image denoising networks. We discuss the complexity of traditional interferometric phase image denoising algorithms to demonstrate the efficiency of the proposed method.