An adaptive speed-identification scheme based on the firefly algorithm (FA) is presented for an air-gap flux vector-controlled (AGFVC) induction motor (IM) drive. The AGFVC IM drive was established using a stator current and air-gap flux. The stator current was acquired from an IM using a Hall effect sensing element. The Hall effect element was employed as an electromagnetic sensor to detect the stator current while the AGFVC IM was rotating under different reversible steady-state speed commands. Model reference adaptive control (MRAC) was utilized to develop a synchronous speed-identification scheme based on the reactive power of the motor, and the rotor speed was estimated by subtracting the slip speed from the estimated synchronous speed. The MRAC adaptation mechanism was designed using the FA. The MATLAB/Simulink © toolbox was used to simulate the proposed AGFVC IM drive system, and all the control algorithms were implemented using a TI DSP 6712-and-F2812 control card to generate pulse width modulation signals through the power stage to actuate the motor. Both simulation and experimental results verified the effectiveness of the proposed system.