In this paper, a time step integration method for resolving the differential equation of motion of discrete structures subjected to dynamic loads is presented. This method is derived based on the approximation of acceleration in two time steps by a combination of both trigonometric cosine and hyperbolic cosine functions with weighted coefficient. The necessary formula of the present method is elaborated for integrating of the governing equation of motion in structural dynamics. The accuracy and stability of the present method are also studied. The numerical results are compared with those obtained using Newmark method, linear acceleration method, showing high effectiveness of the new method.