In this paper, a parallel algorithm of nonlinear dynamic analysis of three-dimensional (3D) reinforced concrete (RC) frame structures based on the platform of graphics processing unit (GPU) is proposed. Time integration is performed using Newmark method for nonlinear implicit dynamic analysis and parallelization strategies are presented. Correspondingly, a parallel Preconditioned Conjugate Gradients (PCG) solver on GPU is introduced for repeating solution of the equilibrium equations for each time step. The RC frames were simulated using fiber beam model to capture nonlinear behaviors of concrete and reinforcing bars. The parallel finite element program is developed utilizing Compute Unified Device Architecture (CUDA). The accuracy of the GPU-based parallel program including single precision and double precision was verified in comparison with ABAQUS. The numerical results demonstrated that the proposed algorithm can take full advantage of the parallel architecture of the GPU, and achieve the goal of speeding up the computation compared with CPU.