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This paper addresses the problem of finding the K nearest neighbors for the trajectory of moving object in the context where the dataset is static and stored in an R-tree. By converted into discovering the K nearest neighbors of the line segment, this kind of query is simplified. Several distance functions between MBRs and line segments are defined and used to prune search space and minimize the pruning distance. Based on branch-and-bound technique and proposed pruning, updating and visiting heuristics, recursive depth-first and heap-based best-first algorithms are presented. An extensive study based on experiments performed with synthetic dataset shows that best-first algorithm outperforms the depth-first algorithm.