Computational sweep analysis of nonlinear ODEs (ordinary differential equations) is of importance in engineering system analysis and design. Sweep analyses usually demand intense computational power according to the number of points and the number of system parameters. This paper presents an efficient parallel algorithm for the sweep analysis of nonlinear ODEs based on graphical processing unit acceleration. The developed method preserves the jump phenomenon characteristics intrinsic to nonlinear ODEs and reduces the effects of irregular computational load. Experiments were realized using Duffing equation by sweeping frequency, amplitude, and equation coefficients. Directly, data parallel implementation and proposed implementations are compared to show the efficiency of the proposed method. Experimental results show that the new method provides significant reductions in the computational durations when compared to sequential implementation.