Plants, which have Right Half Plane (RHP) zero(s), are called as non-minimum phase systems due to their specific phase response characteristics. They have several constraints, such as bandwidth limitation, achievable sensitivity reduction etc., in the design of feedback control systems. Furthermore, the conventional Disturbance Observer (DOB) cannot be directly applied to the non-minimum phase systems due to internal stability problem. This paper proposes a new solution for the robust control problem of non-minimum phase systems by using the DOB. A non-casual, minimum phase transfer function is proposed to remove the internal stability problem in the design of DOB. The Poisson integral formula is used so that the bandwidth constraints of DOB, which occurs due to nonminimum phase characteristic, are analytically derived. The proposed method is applied to a general second order plant model with a RHP zero and system uncertainties. Simulation results are given to show the validity of proposed method.