A variable valve actuating apparatus for an internal combustion engine with an exhaust turbocharger. An intake valve characteristic varying section is arranged to vary an operating angle and a lift of an intake valve. An exhaust valve characteristic varying section is arranged to vary an opening timing and a closing timing of an exhaust valve. In response to an increase in a desired value of an output of the engine, a control section advances an opening timing of the intake valve, retards a closing timing of the intake valve, and advances the opening timing of the exhaust valve. In response to an increase in a boost pressure of the exhaust turbocharger, the control section increases the operating angle and the lift of the intake valve, and retards the opening timing and the closing timing of the exhaust valve.