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 syntax-based 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 form a complete parse tree, 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.