An elevator speed control apparatus includes an inverter connected to an AC power source so as to supply an induction motor for driving an elevator with a variable-voltage, variable-frequency AC. A contactor provided between the invertor and the AC power source. A magnetic flux computing device computes residual value of secondary magnetic flux of the induction motor while the contactor is closed. A control device divides a primary current of the induction motor into an exciting current component and a torque current component so as to perform vector control, this control device being also used to generate a forcing pattern for the exciting current component in accordance with an output of the magnetic flux computing means when the contactor is closed.