The basic requirement of a steganography approach is security against steganalysis attacks. In other words, a steganography method is reliable as long as it withstands all of the known steganalysis approaches. In order to preserve the security of a steganography method, the statistical features of the embedded and the original media must be as close as possible. To achieve this goal, in this paper steganography is applied by introducing the following contributions. Firstly, a new method is suggested to find the most impalpable embedded motion vector (MV). Also, a novel modification cost function with respect to the MVs’ intra-frame and inter-frame statistical differences before and after embedding is proposed for the syndrome-trellis coder. Furthermore, a pseudo-random generator is introduced for altering the arrangement of motion vectors which are used by the syndrome-trellis coder to improve its efficiency. Experimental results show that the proposed method is the most secure MV-based steganography scheme against the state-of-the-art video steganalysis methods as well as preserving other steganography measurements including imperceptibility and compression ratio. Moreover, the computational cost of the proposed scheme is far less than its main rival.