Simultaneous translation is a method to reduce the latency of communication through machine translation (MT) by dividing the input into short segments before performing translation. However, short segments pose problems for syntaxbased translation methods, as it is difficult to generate accurate parse trees for sub-sentential segments. In this paper, we perform the first experiments applying syntax-based SMT to simultaneous translation, and propose two methods to prevent degradations in accuracy: a method to predict unseen syntactic constituents that help generate complete parse trees, and a method that waits for more input when the current utterance is not enough to generate a fluent translation. Experiments on English-Japanese translation show that the proposed methods allow for improvements in accuracy, particularly with regards to word order of the target sentences.