The state-of-the-art solutions for Aspect-Level Sentiment Analysis (ALSA) were built on a variety of deep neural networks (DNN), whose efficacy depends on large amounts of accurately labeled training data. Unfortunately, high-quality labeled training data usually require expensive manual work, and may thus not be readily available in real scenarios. In this paper, we propose a novel solution for ALSA based on the recently proposed paradigm of gradual machine learning, which can enable effective machine labeling without the requirement for manual labeling effort. It begins with some easy instances in an ALSA task, which can be automatically labeled by the machine with high accuracy, and then gradually labels the more challenging instances by iterative factor graph inference. In the process of gradual machine learning, the hard instances are gradually labeled in small stages based on the estimated evidential certainty provided by the labeled easier instances. Our extensive experiments on the benchmark datasets have shown that the performance of the proposed solution is considerably better than its unsupervised alternatives, and also highly competitive compared to the state-of-the-art supervised DNN techniques.