To solve the problems that existing Progressive Mesh (PM) simplification algorithms are facing, such as, loosing key features when meshes are highly simplified, low simplification speed and limited applicability for various models, an edge-collapsing mesh simplification algorithm combining Quadric Error Metric （QEM） and curvature-like Feature value with Variable Parameter (QFVP) was proposed to build progressive meshes for mobile devices. Firstly, the variable parameter w was set to control the relative magnitude of quadratic error and curvature-like value in edge-collapsing error, improving the simplification quality of the algorithm and making the algorithm more applicable. Secondly, an error Back Propagation (BP) neural network was trained to determine the w value of the model. Thirdly, the normal vector linear estimation method in the edge-collapse process was proposed, which shortens the mesh simplification time by 23.7% on average compared to Gouraud estimation method. In the comparison experiments, the PM’s basic meshes generated by QFVP have smaller global error (measured by Hausdorff distance) than those generated by QEM algorithm or Melax algorithm. And QFVP has simplification time about 7.3% longer than QEM algorithm and 54.7% shorter than Melax algorithm.