The classic block-by-block method is a highly efficient numerical method to solve the integral equation. Using the classic block-by-block method, researchers have successfully constructed higher order numerical methods for nonlinear fractional ordinary differential equ-ation, and made preliminary analysis on the convergence of this numerical method. But the results of numerical experiments show that the theoretical analysis does not achieve the optimal error estimate order. Based on the Taylor formula and integral mean value theorem, this article makes a thorough analyses on the block-by-block method of nonlinear fractional ordinary differential equations and obtains the optimal error estimate order. Finally numerical experiments are carried out to support the theoretical claims.