Response time is an important parameter which determines the applied fields and practical vibration reduction effects of magnetorheological (MR) dampers. However, up to now, only a few papers discuss the test and analysis of response times. In this paper, the response time of a large-scale MR damper at different velocities and currents was firstly tested. Then, the transient magnetic field excited by the time-variant excitation current was simulated by finite element method (FEM). Based on the variation of the shear yield stress of magnetorheological fluids in the gap between the cylinder and the piston, the response time of the MR damper was investigated. Influences of eddy current and excitation current response time on the damper's response were also explored. Results show that by utilizing finite elements method, the calculated average effective shear yield strength can be used to predict the response time of a MR damper. Electromagnetic response is the predominant factor influencing the response time of a MR damper, and reducing eddy currents is the key to accelerate the response of a MR damper. Moreover, influence of eddy currents is much larger under stepping down excitation currents than stepping up currents, and with a same magnitude of step, no matter when the current increases or decreases, the smaller the initial current, the greater the eddy current affects a damper's response and the longer the response time of damping force is. A fast response excitation current may induce large eddy currents which reduce the response of the damper instead.