Robust geometric model fitting is an important and challenging research problem in computer vision. It has been widely used in many artificial intelligence related applications, such as lane detection, 3D reconstruction, image stitching and motion segmentation, etc. With the rapid development of the artificial intelligence, the data processed by artificial intelligence systems inevitably contain outliers or noise generated by sensors, environment or human factors. The main task of robust geometric model fitting is to estimate the parameters and the number of model instances from multi-structural data contaminated with outliers and noise. However, the performance of current model fitting methods are far from being satisfactory in practical applications in terms of fitting accuracy and computational speed. In this paper, we propose an efficient model fitting method (NPMF) based on nonnegative matrix underapproximation and pruning techniques, to obtain more accurate fitting results from multi-structural data. The proposed NPMF includes a mismatch pruning algorithm, a model hypothesis pruning algorithm and an improved nonnegative matrix underapproximation algorithm. Firstly, a mismatch pruning algorithm is proposed to alleviate the influence of outliers on the data point sampling process by using a mismatch removal technique, thereby reducing the number of insignificant model hypotheses. After retaining significant model hypotheses by using the weighting scores of model hypotheses, a model hypothesis pruning algorithm is introduced to prune insignificant model hypotheses, and a high-quality nonnegative preference matrix is then constructed. Finally, both the spatial constraint and the sparsity constraint are integrated into the optimization problem of nonnegative matrix underapproximation, and the number and parameters of model instances are adaptively estimated by using a structure merging strategy. The comparison experiments on several representative model fitting methods show that the proposed NPMF obtains better fitting performance and robustness on both synthetic data and real images. For fitting accuracy, the proposed NPMF is about 197.2% and 47.7% higher than T-Linkage and RS-NMU, respectively. For fitting speed, the proposed NPMF is about 2.3 times and 1.9 times faster than T-Linkage and RS-NMU, respectively. Furthermore, the proposed NPMF is about 42.5 times faster than the state-of-the-art MCT for 3D planar surface reconstruction.