Pre-training models have shown their power in sequential recommendation. Recently, prompt has been widely explored and verified for tuning in NLP pre-training, which could help to more effectively and efficiently extract useful knowledge from pre-training models for downstream tasks, especially in cold-start scenarios. However, it is challenging to bring prompt-tuning from NLP to recommendation, since the tokens in recommendation (i.e., items) do not have explicit explainable semantics, and the sequence modeling should be personalized. In this work, we first introduces prompt to recommendation and propose a novel Personalized prompt-based recommendation (PPR) framework for cold-start recommendation. Specifically, we build the personalized soft prefix prompt via a prompt generator based on user profiles and enable a sufficient training of prompts via a prompt-oriented contrastive learning with both prompt- and behavior-based augmentations. We conduct extensive evaluations on various tasks. In both few-shot and zero-shot recommendation, PPR models achieve significant improvements over baselines on various metrics in three large-scale open datasets. We also conduct ablation tests and sparsity analysis for a better understanding of PPR. Moreover, We further verify PPR's universality on different pre-training models, and conduct explorations on PPR's other promising downstream tasks including cross-domain recommendation and user profile prediction.