This paper describes formulation for algorithm of time historical response analysis of vibration for straight-line structure. This method is derived from a combination of the transfer stiffness coefficient method and the Newmark method. And this present method improves the computational accuracy of the transient vibration response analysis remarkably owing to several advantages of the transfer stiffness coefficient method. We regarded the structure as a lumped mass system here. The analysis algorithm for the time historical response was formulated for the straight-line structure containing crooked, tree type system. The validity of the present method compared with the transfer matrix method and the Finite Element Method for transient vibration analysis is demonstrated through the numerical computations.