An optimal control law is derived using a simple integral type quadratic functional. The resulting control scheme is applied to seismically excited non-linear buildings modeled as lumped mass shear frame structures. The non-linearity is reflected by the non-linear stiffness restoring force. Active tendon actuators are considered as control devices. The performance of the proposed control is compared to those of the uncontrolled structure and the passive base isolation. It is shown by numerical simulation results that the proposed control is capable of suppressing the uncontrolled seismic vibrations of the non-linear structures.