Series elastic actuators (SEAs) are widely used as mechanical drives in robots that intelligently interact with environments and humans. Specific to these applications, a novel finite time output feedback controller (FTOFC) is presented to generate the desired torque. In particular, the generic dynamics of SEA systems is described and some analysis and transformation operations are performed. Then based on the recently developed finite-time control technique, a finite time observer and a continuous second order sliding-mode control scheme are introduced to synthesize the control law, on the basis of which some theoretical analysis is implemented to show the stability and boundedness of the closed-loop signals. Compared with existing methods, the contribution of the paper is three-fold:1) the controller is suitable for nonlinear SEAs, which implies it is more generic; 2) the finite-time convergence property is guaranteed to have a better transient performance; 3) the controller works well even in the presence of unknown payload parameters and external disturbances. To demonstrate these merits, some experiments are carried out on the self-built single-joint SEA robot. The experimental results show that the designed controller achieves better performance than the traditional cascade-PID controller, in terms of robustness against system uncertainties.