This paper presents a new method to estimate maximum drifts, relative displacements between adjacent floors, of all stories of multi-degree-of-freedom (MDOF) shear structures using only one floor’s absolute acceleration time history response under the ground excitation. The absolute acceleration and relative displacement are formulated in modal coordinates and the state-space expression is derived. Then the numerical simulation for a three-story structure was conducted to verify the performance of the state-space equation. The comparison of the estimated state and input with actual values is made and shows the good agreement. In addition, the relative displacement time histories of all floors were obtained, and the errors of maximum displacements and inter-story drifts were analyzed. The robustness against environmental noise was also investigated by numerical simulations as well. The results of simulations indicate the estimation is satisfactory, and very robust against the environmental disturbance.