Abstract: In order to calculate structural dynamic response, a new step-by-step integration is presented.The step-by-step recursion method is deduced on the basis of uniform quintic B-spline interpolation of nodal displacement, velocity, and acceleration within a local time domain.Two parameters are introduced to meet good stability and accuracy.The proposed method has advantages of self-starting and no middle computational procedure.The numerical results and the comparison with Newmark and Wilson method show this method possesses high calculation accuracy.