In this paper we present a novel unsupervised representation learning approach for 3D shapes, which is an important research challenge as it avoids the manual effort required for collecting supervised data. Our method trains an RNN-based neural network architecture to solve multiple view inter-prediction tasks for each shape. Given several nearby views of a shape, we define view inter-prediction as the task of predicting the center view between the input views, and reconstructing the input views in a low-level feature space. The key idea of our approach is to implement the shape representation as a shape-specific global memory that is shared between all local view inter-predictions for each shape. Intuitively, this memory enables the system to aggregate information that is useful to better solve the view inter-prediction tasks for each shape, and to leverage the memory as a view-independent shape representation. Our approach obtains the best results using a combination of L_2 and adversarial losses for the view inter-prediction task. We show that VIP-GAN outperforms state-of-the-art methods in unsupervised 3D feature learning on three large scale 3D shape benchmarks.