Efficient predicate matching is essential to provide real-time responses in data stream processing. Many predicate indexes have been introduced to address the predicate matching problem. Among them, the IBS-tree handles predicates with open and closed intervals in O(log2n) time. However, it was found that its insertion algorithm is not optimal when processing open intervals. In this paper, a predicate indexing method is proposed that supports fast insertion of predicates based on the IBS-tree scheme without degrading the search performance. The basic idea of the proposed method is to use shared lists when processing open intervals, and the insertion time is reduced to O(log n) in this case. When dealing with closed intervals, an algorithm of the IBS-tree was used. Consequently, the insertion performance of the proposed method improves as the ratio of open intervals increases, which we observed through our experiments.