This paper proposes an acceleration-based robust controller for the motion control problem, i.e., position and force control problems, of a novel series elastic actuator (SEA). A variable stiffness SEA is designed by using soft and hard springs in series so as to relax the fundamental performance limitation of conventional SEAs. Although the proposed SEA intrinsically has several superiorities in force control, its motion control problem, especially position control problem, is harder than conventional stiff and SEAs due to its special mechanical structure. It is shown that the performance of the novel SEA is limited when conventional motion control methods are used. The performance of the steady-state response is significantly improved by using disturbance observer (DOb), i.e., improving the robustness; however, it degrades the transient response by increasing the vibration at tip point. The vibration of the novel SEA and external disturbances are suppressed by using resonance ratio control (RRC) and arm DOb, respectively. The proposed method can be used in the motion control problem of conventional SEAs as well. The intrinsically safe mechanical structure and high-performance motion control system provide several benefits in industrial applications, e.g., robots can perform dexterous and versatile industrial tasks alongside people in a factory setting. The experimental results show viability of the proposals.