How can we extend a pre-trained model to many language understanding tasks, without labeled or additional unlabeled data? Pre-trained language models (PLMs) have been effective for a wide range of NLP tasks. However, existing approaches either require fine-tuning on downstream labeled datasets or manually constructing proper prompts. In this paper, we propose nonparametric prompting PLM (NPPrompt) for fully zero-shot language understanding. Unlike previous methods, NPPrompt uses only pre-trained language models and does not require any labeled data or additional raw corpus for further fine-tuning, nor does it rely on humans to construct a comprehensive set of prompt label words. We evaluate NPPrompt against previous major few-shot and zero-shot learning methods on diverse NLP tasks: including text classification, text entailment, similar text retrieval, and paraphrasing. Experimental results demonstrate that our NPPrompt outperforms the previous best fully zero-shot method by big margins, with absolute gains of 12.8% in accuracy on text classification and 18.9% on the GLUE benchmark.