Abstract: In order to compute electrically large scatterers rapidly and accurately with less computational cost a multilevel fast physical optics (MLFPO) method based on an octree multilevel structure and quadratic mesh technique is proposed in this work. The octree multilevel technique makes full use of parallel techniques to further accelerate the computation. Additionally, the quadratic mesh technique provides a better fit to the surface of convex scatterers and reduces the number of unknowns compared with planar triangular patches effectively. Furthermore, this work extends the application of the MLFPO method from PEC to complex multilayer coated targets. Numerical examples demonstrate that the mean error of the PO and MLFPO method is within 1.54 dB in the S, C, X, and Ku bands. Compared to the PO method in the commercial software FEKO, the computational speed of the MLFPO method increases more than 8 times and the computational storage reduces 98%. The MLFPO method reduces computational costs while ensuring calculation accuracy, making it an efficient method for analyzing the electromagnetic scattering problem of electrically large smooth convex scatterers.