An initial position estimating apparatus for estimating an initial position of a rotor of a permanent-magnet synchronous motor, the apparatus comprising: a signal processor configured to output an angular error component from a change amount of a q-axis current in an estimated rotor reference frame; a position estimator configured to estimate an electrical position of the rotor from the angular error component; a magnetic pole determination portion configured to output magnetic pole determination information according to a sign of a magnetic pole determination signal determined based on a change amount of a d-axis current in the estimated rotor reference frame and based on a d-axis voltage; and a first addition portion configured to output an initial position of the rotor by adding the magnetic pole determination information to the electrical position, characterized in that the magnetic pole determination portion includes: a fourth delay portion configured to delay the d-axis voltage; a second sign determination portion configured to determine a sign of the delayed d-axis voltage; a fourth operation portion configured to multiply the sign of the delayed d-axis voltage by the change amount of the d-axis current; a fifth operation portion configured to multiply an output of the fourth operation portion by the d-axis voltage; and an integrator configured to integrate an output of the fifth operation portion and thereby output the magnetic pole determination signal. a signal processor configured to output an angular error component from a change amount of a q-axis current in an estimated rotor reference frame; a position estimator configured to estimate an electrical position of the rotor from the angular error component; a magnetic pole determination portion configured to output magnetic pole determination information according to a sign of a magnetic pole determination signal determined based on a change amount of a d-axis current in the estimated rotor reference frame and based on a d-axis voltage; and a first addition portion configured to output an initial position of the rotor by adding the magnetic pole determination information to the electrical position, characterized in that the magnetic pole determination portion includes: a fourth delay portion configured to delay the d-axis voltage; a second sign determination portion configured to determine a sign of the delayed d-axis voltage; a fourth operation portion configured to multiply the sign of the delayed d-axis voltage by the change amount of the d-axis current; a fifth operation portion configured to multiply an output of the fourth operation portion by the d-axis voltage; and an integrator configured to integrate an output of the fifth operation portion and thereby output the magnetic pole determination signal. a fourth delay portion configured to delay the d-axis voltage; a second sign determination portion configured to determine a sign of the delayed d-axis voltage; a fourth operation portion configured to multiply the sign of the delayed d-axis voltage by the change amount of the d-axis current; a fifth operation portion configured to multiply an output of the fourth operation portion by the d-axis voltage; and an integrator configured to integrate an output of the fifth operation portion and thereby output the magnetic pole determination signal. <EOS>