This paper proposes a method for intrasentential subject zero anaphora resolution in Japanese. Our proposed method utilizes a Multi-column Convolutional Neural Network (MCNN) for predicting zero anaphoric relations. Motivated by Centering Theory and other previous works, we exploit as clues both the surface word sequence and the dependency tree of a target sentence in our MCNN. Even though the F-score of our method was lower than that of the state-of-the-art method, which achieved relatively high recall and low precision, our method achieved much higher precision (> 0.8) in a wide range of recall levels. We believe such high precision is crucial for real-world NLP applications and thus our method is preferable to the state-of-the-art method.