This paper presents a new approach to measuring similarity over massive time-series data. Our approach is built on two principles: one is to parallelize the large amount computation using a scalable cloud serving system, called TimeCloud. The another is to benefit from the filter-and-refinement approach for query processing, such that similarity computation is efficiently performed over approximated data at the filter step, and then the following refinement step measures precise similarities for only a small number of candidates resulted from the filtering. To this end, we establish a set of firm theoretical backgrounds, as well as techniques for processing kNN queries. Our experimental results suggest that the approach proposed is efficient and scalable.