DC-biased sinusoidal current excited flux modulated doubly-salient reluctance motor (FMDRM) drives are developed to reduce the torque ripple and vibration of doubly-salient reluctance motors (DRMs). Conventionally, because of the discontinuous quasi-square current excitation, the rotor position of DRMs is estimated by the combination of piecewise estimation of phase angle information for each phase, where the continuous position estimation for the novel FMDRM drives cannot be realized. To solve this issue, this paper proposes a continuous rotor position estimation strategy for FMDRM drives based on back electromotive force (back-EMF) harmonic characteristics. Firstly, the back-EMF harmonics caused by the rotor saliency and their relationship with the rotor position are analyzed in detail. Then, the corresponding harmonic current regulator and quadrature signal generator are investigated to achieve harmonic current suppression and obtain the quadrature harmonic back-EMF components in the rotating reference frame for rotor position estimation simultaneously. Furthermore, a virtual-inductance-based method is developed to calibrate the phase angle offset between the estimated and actual rotor positions. With the proposed scheme, accurate continuous rotor position estimation can be achieved without any additional hardware. Experimental validations are presented on a three-phase 12/8 FMDRM prototype to verify the accuracy of the proposed rotor position estimation scheme.