Disclosed herein are a motor driving apparatus and a controlling method thereof. The motor driving apparatus includes a motor having a rotor including a permanent magnet, and a stator, an inverter to supply a driving power to the motor, and a control unit to estimate a parameter using a startup estimation when a rotation speed of the rotor is less than a preset startup speed, to estimate the parameter using a driving estimation with compensating for a dead time when the rotation speed of the rotor is equal to or greater than the preset startup speed and a torque of the rotor is equal to or less than a preset driving torque, and to estimate the parameter using the driving estimation without the dead time compensation when the rotation speed of the rotor is equal to or greater than the preset startup speed and the torque of the rotor exceeds the preset driving torque.