Autonomous exploration is a crucial aspect of robotics, enabling robots to explore unknown environments and generate maps without prior knowledge. This paper proposes a method to enhance exploration efficiency by integrating neural network-based occupancy grid map prediction with uncertainty-aware Bayesian neural network. Uncertainty from neural network-based occupancy grid map prediction is probabilistically integrated into mutual information for exploration. To demonstrate the effectiveness of the proposed method, we conducted comparative simulations within a frontier exploration framework in a realistic simulator environment against various information metrics. The proposed method showed superior performance in terms of exploration efficiency.