In lithography， the uniformity of resist coating considerably affects the consistency of line width after spin-coating. To obtain homogeneity of the resist-layer thickness on the upper surface of a curved substrate， a hydrodynamic model of a non-Newtonian fluid element is first established on the surface of the curved substrate under spin-coating. According to the corresponding boundary conditions and constitutive equation and continuity equation of the non-Newtonian fluid， the relationship between the nature of the fluid， curvature radius of the surface， horizontal vector radius， rotation speed and time， and the final thickness of the fluid is deduced and obtained. Second， a rheometer is used to calibrate the fluid viscosity of 950 K PMMA C 2% resist. A spin-coating experiment is conducted on a curved substrate using rotational velocity as a single variable. After centrifugation， the thickness was measured by ellipsometry. The relationship between the resist-layer thickness and the change in the vector radius is obtained and demonstrated with theoretical results. Experimental results show that when the spin speed is 2 000 r/min， the theoretical thickness is 267 nm， measured thickness is 230 nm， and deviation ratio is 13.86%. When the spin speed is 3 000 r/min， the theoretical thickness is 178 nm， measured thickness is 172 nm， and deviation ratio is 3.37%. After spin-coating， the soft-bake will further reduce the thickness of the resist-layer，and the deviation is within the normal range. Therefore， the mathematical model can provide a theoretical guidance for homogeneity after spin-coating， and the established model has a good predictability.