Massive datasets of spatial trajectories representing the mobility of a diversity of moving objects are ubiquitous in research and industry. Similarity search of a large collection of trajectories is indispensable for turning these datasets into knowledge. Locality sensitive hashing (LSH) is a powerful technique for fast similarity searches. Recent methods employ LSH and attempt to realize an efficient similarity search of trajectories; however, those methods are inefficient in terms of search time and memory when applied to massive datasets. To address this problem, we present the trajectory-indexing succinct trit-array trie (tSTAT), which is a scalable method leveraging LSH for trajectory similarity searches. tSTAT quickly performs the search on a tree data structure called trie. We also present two novel techniques that enable to dramatically enhance the memory efficiency of tSTAT. One is a node reduction technique that substantially omits redundant trie nodes while maintaining the time performance. The other is a space-efficient representation that leverages the idea behind succinct data structures (i.e., a compressed data structure supporting fast data operations). We experimentally test tSTAT on its ability to retrieve similar trajectories for a query from large collections of trajectories and show that tSTAT performs superiorly in comparison to state-of-the-art similarity search methods.