This paper proposes a new position sensorless drive for brushless DC (BLDC) motors. Typical sensorless control methods such as the scheme with the back-EMF detection method show high performance only at a high speed range because the magnitude of the back-EMF is dependent upon the rotor speed. This paper presents a new solution that estimates the rotor position by using an unknown input observer over a full speed range. In the proposed method, a trapezoidal back-EMF is modelled as an unknown input and the proposed unknown input observer estimating a line-to-line back-EMF in real time makes it possible to detect the rotor position. In particular, this observer has high performance at a low speed range in that the information of a rotor position is calculated independently of the rotor speed without an additional circuit or complicated operation process. Simulations and experiments have been carried out for the verification of the proposed control scheme.