The equivalent circuit of a voltage source inverter (VSI) fed brushless DC (BLDC) motor is similar to a buck converter supplied brushed DC motor. This analogy derives a linear relationship between the duty ratio and motor speed for continuous current conduction mode (CCCM). However, this relationship is not linear for discontinuous current conduction mode (DCCM), which is not generally considered in literature while controllers are designed. The DCCM of the BLDC motor driven by unipolar pulse width modulation (PWM) controlled voltage source inverter is analyzed, and corresponding quasi-steady-state model is derived in this paper. The motor speed can be precisely determined by simple computations with the proposed DCCM model, which can lead to complexity reduction in controller design. The effectiveness of the proposed model has been validated by the simulation and experimental analysis.