Abstractive document summarization is usually modeled as a sequence-to-sequence (SEQ2SEQ) learning problem. Unfortunately, training large SEQ2SEQ based summarization models on limited supervised summarization data is challenging. This paper presents three sequence-to-sequence pre-training (in shorthand, STEP) objectives which allow us to pre-train a SEQ2SEQ based abstractive summarization model on unlabeled text. The main idea is that, given an input text artificially constructed from a document, a model is pre-trained to reinstate the original document. These objectives include sentence reordering, next sentence generation and masked document generation, which have close relations with the abstractive document summarization task. Experiments on two benchmark summarization datasets (i.e., CNN/DailyMail and New York Times) show that all three objectives can improve performance upon baselines. Compared to models pre-trained on large-scale data (larger than 160GB), our method, with only 19GB text for pre-training, achieves comparable results, which demonstrates its effectiveness.