A bottleneck problem with Chinese named entity recognition (NER) in new domains is the lack of annotated data. One solution is to utilize the method of distant supervision, which has been widely used in relation extraction, to automatically populate annotated training data without humancost. The distant supervision assumption here is that if a string in text is included in a predefined dictionary of entities, the string might be an entity. However, this kind of auto-generated data suffers from two main problems: incomplete and noisy annotations, which affect the performance of NER models. In this paper, we propose a novel approach which can partially solve the above problems of distant supervision for NER. In our approach, to handle the incomplete problem, we apply partial annotation learning to reduce the effect of unknown labels of characters. As for noisy annotation, we design an instance selector based on reinforcement learning to distinguish positive sentences from auto-generated annotations. In experiments, we create two datasets for Chinese named entity recognition in two domains with the help of distant supervision. The experimental results show that the proposed approach obtains better performance than the comparison systems on both two datasets.