The rise of deep learning technique has raised new privacy concerns about the training data and test data. In this work, we investigate the model inversion problem in the adversarial settings, where the adversary aims at inferring information about the target model's training data and test data from the model's prediction values. We develop a solution to train a second neural network that acts as the inverse of the target model to perform the inversion. The inversion model can be trained with black-box accesses to the target model. We propose two main techniques towards training the inversion model in the adversarial settings. First, we leverage the adversary's background knowledge to compose an auxiliary set to train the inversion model, which does not require access to the original training data. Second, we design a truncation-based technique to align the inversion model to enable effective inversion of the target model from partial predictions that the adversary obtains on victim user's data. We systematically evaluate our inversion approach in various machine learning tasks and model architectures on multiple image datasets. Our experimental results show that even with no full knowledge about the target model's training data, and with only partial prediction values, our inversion approach is still able to perform accurate inversion of the target model, and outperform previous approaches.