This paper explores the use of Deep Learning methods for automatic estimation of quality of human translations. Automatic estimation can provide useful feedback for translation teaching, examination and quality control. Conventional methods for solving this task rely on manually engineered features and external knowledge. This paper presents an end-to-end neural model without feature engineering, incorporating a cross attention mechanism to detect which parts in sentence pairs are most relevant for assessing quality. Another contribution concerns of prediction of fine-grained scores for measuring different aspects of translation quality. Empirical results on a large human annotated dataset show that the neural model outperforms feature-based methods significantly. The dataset and the tools are available.