This paper addresses the modified Dynamic Relaxation algorithm, called mdDR by minimizing displacement error between two successive iterations. In the mdDR method, new relationships for fictitious mass and damping are presented. The results obtained from linear and nonlinear structural analysis, either by finite element or finite difference techniques; demonstrate the potential ability of the proposed scheme compared to the conventional DR algorithm. It is shown that the mdDR improves the convergence rate of Dynamic Relaxation method without any additional calculations, so that, the cost and computational time are decreased. Simplicity, high efficiency and automatic operations are the main merits of the proposed technique.