Visual localization plays a critical role in the functionality of low-cost autonomous mobile robots. Current state-of-the-art approaches for achieving accurate visual localization are 3D scene-specific, requiring additional computational and storage resources to construct a 3D scene model when facing a new environment. An alternative approach of directly using a database of 2D images for visual localization offers more flexibility. However, such methods currently suffer from limited localization accuracy. In this paper, we propose an accurate and robust multiple checking-based 3D model-free visual localization system to address the aforementioned issues. To ensure high accuracy, our focus is on estimating the pose of a query image relative to the retrieved database images using 2D-2D feature matches. Theoretically, by incorporating the local planar motion constraint into both the estimation of the essential matrix and the triangulation stages, we reduce the minimum required feature matches for absolute pose estimation, thereby enhancing the robustness of outlier rejection. Additionally, we introduce a multiple-checking mechanism to ensure the correctness of the solution throughout the solving process. For validation, qualitative and quantitative experiments are performed on both simulation and two real-world datasets and the experimental results demonstrate a significant enhancement in both accuracy and robustness afforded by the proposed 3D model-free visual localization system.