Conventional autoregressive left-to-right (L2R) sequence generation faces two issues during decoding: limited to unidirectional target sequence modeling, and constrained on strong local dependencies. To address the aforementioned problem, we propose P$^3$LM, a probabilistically permuted prophet language model, which strengthens the modeling of bidirectional information and long token dependencies for sequence generation. Specifically, P$^3$LM learns to generate tokens in permuted order upon an order-aware transformer decoder, as well as to generate the corresponding future $N$ tokens with a multi-stream attention mechanism. Extensive experiments are conducted on the GLGE benchmark, which includes four datasets for summarization, two for question generation, one for conversational question answering, and one for dialog response generation, where P$^3$LM achieves state-of-the-art results compared with strong publicly available generative pre-training methods.