Although the grid with film sphere and porous structure plays a very important role in sphere grid-controlled electron gun, its cut-off amplification factor can be obtained only in the plane-square-mesh approximation. Due to the lack of consideration for non-uniformity of cut-off amplification factor and information about cathode half-angle and radius of curvature of grid, the designs of sphere grid and electron gun cannot be related by the plane-square-mesh approximation, which is unusable as theory basis for fabricating thinner grid wires. In this paper, we model the grid with film sphere and porous structure and obtain the new expression for cut-off amplification factor by recalculating the screening factors and the ratios of the radius of grid wire to the area of this single mesh in different ring areas. In combination with the conclusion of cut-off amplification factor given in Spangenberg's book, the effects of grid wire's radius, sphere center angle and the number of radial grid wires on the cut-off amplification factor, and the variation of the cut-off amplification factor with temperature rising are obtained. Finally, the steps for the design of grid with film sphere and porous structure and some specific examples are presented. The results show that the grid devised by new expression is more stable and reliable, and problems existing in plane-square-mesh approximation are solved.