A method for starting an engine for a hybrid electric vehicle that includes a starter connected to the engine by a gear to start the engine and a motor-generator connected to the engine by a belt to start the engine or produce electricity include determining whether a start signal is input, determining whether a predetermined cold start condition is satisfied when it is determined that the start signal is input, starting the engine by use of the starter in a predetermined cold start mode when the cold start condition is satisfied, determining whether a predetermined cooperative control start condition is satisfied when the cold start condition is not satisfied, and starting the engine by use of the starter and the motor-generator in a predetermined cooperative control start mode when the cooperative control start condition is satisfied.