The berth allocation problem is one of the important problems in the maritime ship operations. Efficient sea transportation can be realized by optimizing the berth operation schedule. The dynamic berth allocation problem asks to determine the allocation and berthing time of each vessel to the berth that minimizes the total service time given a set of vessels and a set of berths. The branch and bound algorithms have been used to solve the problem as an exact solution algorithm. However, it becomes intractable to solve the problem by the conventional branch and bound algorithms when the number of ships and berths is increased. In this paper, we propose a new branch-and-bound algorithm called Neural Network Assisted Branch-and-Bound (NN-BB) to determine the search priority of each node to reduce the total computation time of the branch-and-bound method. By determining the search priority of the node from the result of the neural network, the optimal solution is quickly searched for the learned problem. We compare the performance of the proposed method with the conventional branch and bound method from computational experiments.