Usually considered as a classification problem, entity resolution (ER) can be very challenging on real data due to the prevalence of dirty values. The state-of-the-art solutions for ER were built on a variety of learning models (most notably deep neural networks), which require lots of accurately labeled training data. Unfortunately, high-quality labeled data usually require expensive manual work, and are therefore not readily available in many real scenarios. In this paper, we propose a novel learning paradigm for ER, called gradual machine learning, which aims to enable effective machine labeling without the requirement for manual labeling effort. It begins with some easy instances in a task, which can be automatically labeled by the machine with high accuracy, and then gradually labels more challenging instances by iterative factor graph inference. In gradual machine learning, the hard instances in a task are gradually labeled in small stages based on the estimated evidential certainty provided by the labeled easier instances. Our extensive experiments on real data have shown that the performance of the proposed approach is considerably better than its unsupervised alternatives, and highly competitive compared to the state-of-the-art supervised techniques. Using ER as a test case, we demonstrate that gradual machine learning is a promising paradigm potentially applicable to other challenging classification tasks requiring extensive labeling effort.