Anaphora resolution is one of the most important research topics in Natural Language Processing. In English, overt pronouns such as she and definite noun phrases such as the company are anaphors that refer to preceding entities (antecedents). In Japanese, anaphors are often omitted, and these omissions are called zero pronouns. There are two major approaches to zero pronoun resolution: the heuristic approach and the machine learning approach. Since we have to take various factors into consideration, it is difficult to find a good combination of heuristic rules. Therefore, the machine learning approach is attractive, but it requires a large amount of training data. In this paper, we propose a method that combines ranking rules and machine learning. The ranking rules are simple and effective, while machine learning can take more factors into account. From the results of our experiments, this combination gives better performance than either of the two previous approaches.