Pre-training has been adopted in a few of recent works for Vision-and-Language Navigation (VLN). However, previous pre-training methods for VLN either lack the ability to predict future actions or ignore the trajectory contexts, which are essential for a greedy navigation process. In this work, to promote the learning of spatio-temporal visual-textual correspondence as well as the agent's capability of decision making, we propose a novel history-and-order aware pre-training paradigm (HOP) with VLN-specific objectives that exploit the past observations and support future action prediction. Specifically, in addition to the commonly used Masked Language Modeling (MLM) and Trajectory-Instruction Matching (TIM), we design two proxy tasks to model temporal order information: Trajectory Order Modeling (TOM) and Group Order Modeling (GOM). Moreover, our navigation action prediction is also enhanced by introducing the task of Action Prediction with History (APH), which takes into account the history visual perceptions. Extensive experimental results on four downstream VLN tasks (R2R, REVERIE, NDH, RxR) demonstrate the effectiveness of our proposed method compared against several state-of-the-art agents.