This paper presents a novel video stabilization approach by leveraging the multiple planes structure of video scene to stabilize inter-frame motion. As opposed to previous stabilization procedure operating in a single plane, our approach primarily deals with multiplane videos and builds their multiple planes structure for performing stabilization in respective planes. Hence, a robust plane detection scheme is devised to detect multiple planes by classifying feature trajectories according to reprojection errors generated by plane induced homographies. Then, an improved planar stabilization technique is applied by conforming to the compensated homography in each plane. Finally, multiple stabilized planes are coherently fused by content-preserving image warps to obtain the output stabilized frames. Our approach does not need any stereo reconstruction, yet is able to produce commendable results due to awareness of multiple planes structure in the stabilization. Experimental results demonstrate the effectiveness and efficiency of our approach to robust stabilization on multiplane videos.