An efficient predictor algorithm is presented for fast geometrically-nonlinear dynamic analysis. The basic concept of this algorithm entails the use of the predicted starting point close to the converged solution point in the iterative procedure of nonlinear dynamics. The predicted starting point is much closer to the converged solution than the conventionally adopted starting point, i.e. the previously converged solution point, so the number of iterations required for convergence decreases. In addition, the additional time for prediction is trivial, and therefore, the total computation time significantly decreases. The neural network which is used to predict the starting point characterizes the pattern of the previously converged solution points. The mean vector, the complementary vector, and the slope factor are elements of the present predictor algorithm, which work with the neural network to make the prediction in the iterative procedure of nonlinear dynamic analysis. Numerical tests of structural nonlinear dynamic problems using an 18-node assumed strain solid element demonstrate the validity and the efficiency of the predictor algorithm.