This paper presents the design of second-order sliding mode controllers for semi-active control using magneto-rheological (MR) dampers. The approach can be useful in applications involving shock absorbers but here our main concern is the suppression of building vibrations induced by dynamic loadings such as earthquakes or strong winds. The MR dampers have been of increasing interest in structural control as they are inexpensive to manufacture and have attractive properties such as small energy requirements, reliability and stability in operations, as well as a fast response of milliseconds. Challenges of MR damper structural control rest with the systems high nonlinearity due to the force-velocity hysteresis, and the constraint of the magnetisation current, required to be between its zero and maximal values. A variety of control algorithms have been applied, including the decentralized bangbang control, modulated homogeneous friction algorithm, clipped optimal control, Lyapunov-based control, and also non model-based intelligent schemes. In these techniques, the currents are usually obtained from the damping force indirectly rather than directly from the controller output. For direct current control, in this paper we propose second-order sliding mode controllers, which can satisfy the control constraint, provide high accuracy, retain robustness and remove chattering. The effectiveness of the proposed direct current control technique is verified, in simulations, on a benchmark building model subject to excitation of various scaled earthquake records.