In this paper, we propose a new indexing structure for parameterized strings which we call PLSTs, by generalizing linear-size suffix tries for ordinary strings. Two parameterized strings are said to match if there is a bijection on the symbol set that makes the two coincide. PLSTs are applicable to the parameterized pattern matching problem, which is to decide whether the input parameterized text has a substring that matches the input parameterized pattern. The size of PLSTs is linear in the text size, with which our algorithm solves the parameterized pattern matching problem in linear time in the pattern size. PLSTs can be seen as a compacted version of parameterized suffix tries and a combination of linear-size suffix tries and parameterized suffix trees. We experimentally show that PLSTs are more space efficient than parameterized suffix trees for highly repetitive strings.