Existing index structures for multivariate time series can't support similarity search under DTW distance efficiently. Firstly, a transformation method, which converts unequal-length multivariate time series into equal-length univariate time series, is proposed and a mathematical proof that the transformation satisfies lower bounding distance lemma is provided. Secondly, DTW lower bounding distance is proposed, and its character is analyzed. Thirdly, based on DTW lower bounding distance proposed above, an index structure for multivariate time series is proposed, allowing database of multivariate time series be organized. Further, similarity search algorithm and process for multivariate time series are discussed, and related mathematical proofs that false dismissals can be avoided are given. Finally, validity of proposed method is verified by experiments.