Dependency tree-to-tree translation models are powerful because they can naturally handle long range reorderings which is important for distant language pairs. The translation process is easy if it can be accomplished only by replacing non-terminals in translation rules with other rules. However it is sometimes necessary to adjoin translation rules. Flexible non-terminals have been proposed as a promising solution for this problem. A flexible non-terminal provides several insertion position candidates for the rules to be adjoined, but it increases the computational cost of decoding. In this paper we propose a neural network based insertion position selection model to reduce the computational cost by selecting the appropriate insertion positions. The experimental results show the proposed model can select the appropriate insertion position with a high accuracy. It reduces the decoding time and improves the translation quality owing to reduced search space.