An apparatus and a method to detect an offset of a motor position sensor. The apparatus includes a command voltage vector generation unit configured to, in a state in which a motor has been coupled to an electric booster braking system, generate a command voltage vector having a predefined command phase and command voltage and apply the command voltage vector to the motor such that a piston moves in a direction determined based on the current position of the piston, and an offset detection unit configured to detect the offset of the motor position sensor based on a phase difference between a command phase of the command voltage vector and an actually measured phase obtained by actually measuring, by the motor position sensor, a phase formed by rotors of the motor that are aligned as the command voltage vector is applied from the command voltage vector generation unit to the motor.