Ensuring safety and motion consistency for robot navigation in occluded, obstacle-dense environments is a critical challenge. In this context, this study presents an occlusion-aware Consistent Model Predictive Control (CMPC) strategy. To account for the occluded obstacles, it incorporates adjustable risk regions that represent their potential future locations. Subsequently, dynamic risk boundary constraints are developed online to enhance safety. Based on these constraints, the CMPC constructs multiple locally optimal trajectory branches (each tailored to different risk regions) to strike a balance between safety and performance. A shared consensus segment is generated to ensure smooth transitions between branches without significant velocity fluctuations, preserving motion consistency. To facilitate high computational efficiency and ensure coordination across local trajectories, we use the alternating direction method of multipliers (ADMM) to decompose the CMPC into manageable sub-problems for parallel solving. The proposed strategy is validated through simulations and real-world experiments on an Ackermann-steering robot platform. The results demonstrate the effectiveness of the proposed CMPC strategy through comparisons with baseline approaches in occluded, obstacle-dense environments.