Interactive-predictive machine translation (IPMT) is a translation mode which combines machine translation technology and human behaviours. In the IPMT system, the utilization of the prefix greatly affects the interaction efficiency. However, state-of-the-art methods filter translation hypotheses mainly according to their matching results with the prefix on character level, and the advantage of the prefix is not fully developed. Focusing on this problem, this paper mines the deep constraints of prefix on syntactic level to improve the performance of IPMT systems. Two syntactic subtree matching rules based on phrase structure grammar are proposed to filter the translation hypotheses more strictly. Experimental results on LDC Chinese-English corpora show that the proposed method outperforms state-of-the-art phrase-based IPMT system while keeping comparable decoding speed.