Aiming at the problem of strong reflection and multiple reflection in 3D measurement of industrial shiny parts, a technology based on high-dynamic range N-step fringe projection profilometry and single pixel imaging were developed, which effectively solved the problems of point cloud missing and accuracy degradation. Two methods were used to measure standard gauge blocks. The root mean square error of method based on high-dynamic range N-step fringe projection profilometry is 0.0066 mm. The root mean square error of method based on single pixel imaging is 0.0046 mm. With the step standard as the target, the absolute accuracy verification experiment was carried out. The absolute deviation is less than 0.007 mm. The proposed method was used to measure aero-engine impeller, turbine blade, and carbon fiber structures. Experimental results demonstrated that the proposed method combining high dynamic range N-step fringe projection profilometry and single pixel imaging can avoid point cloud missing. The complete data can be obtained in both strong reflection and multiple reflection areas. The proposed method has realized accurate 3D measurement of industrial shiny parts.