Background modeling of video frame sequences is a prerequisite for computer vision applications. Robust principal component analysis(RPCA), which aims to recover low rank matrix in applications of data mining and machine learning, has shown improved background modeling performance. Unfortunately, The traditional RPCA method considers the batch recovery of low rank matrix of all samples, which leads to higher storage cost. This paper proposes a novel online motion-aware RPCA algorithm, named OM-RPCAT, which adopt truncated nuclear norm regularization as an approximation method for of low rank constraint. And then, Two methods are employed to obtain the motion estimation matrix, the optical flow and the frame selection, which are merged into the data items to separate the foreground and background. Finally, an efficient alternating optimization algorithm is designed in an online manner. Experimental evaluations of challenging sequences demonstrate promising results over state-of-the-art methods in online application.