Biomedical named entity recognition (BioNER) is a fundamental step for mining COVID-19 literature. Existing BioNER datasets cover a few common coarse-grained entity types (e.g., genes, chemicals, and diseases), which cannot be used to recognize highly domain-specific entity types (e.g., animal models of diseases) or emerging ones (e.g., coronaviruses) for COVID-19 studies. We present CORD-NER, a fine-grained named entity recognized dataset of COVID-19 literature (up until May 19, 2020). CORD-NER contains over 12 million sentences annotated via distant supervision. Also included in CORD-NER are 2,000 manually-curated sentences as a test set for performance evaluation. CORD-NER covers 75 fine-grained entity types. In addition to the common biomedical entity types, it covers new entity types specifically related to COVID-19 studies, such as coronaviruses, viral proteins, evolution, and immune responses. The dictionaries of these fine-grained entity types are collected from existing knowledge bases and human-input seed sets. We further present DISTNER, a distantly supervised NER model that relies on a massive unlabeled corpus and a collection of dictionaries to annotate the COVID-19 corpus. DISTNER provides a benchmark performance on the CORD-NER test set for future research.