Routing is a crucial step for modern VLSI designs, and a typical router often uses a maze routing algorithm to re-route each congested net iteratively until the solution converges. The new path found by the router at each iteration in general will be discarded if it does not have a lower routing cost than the current one. In this paper, we aim to predict whether the path generated by a maze router has a routing cost less than a given bound. This prediction problem is transformed into a binary classification problem for which a convolutional neural network (CNN) is trained. We extracted the routing results of an academic global router from more than a dozen circuits, and used them to train and test our CNN model. The experiments show that our CNN model can reach 78.2% prediction accuracy while the prediction is more than two times faster than maze routing on average.