A method and an apparatus for starting an engine of a mild hybrid electric vehicle are disclosed. A method for starting an engine of a mild hybrid electric vehicle includes operating a mild hybrid starter & generator (MHSG) to perform an engine cranking operation, calculating an aging factor of the engine based on a time to reach a target RPM, calculating a moving average value of the aging factor, determining whether the moving average value of the aging factor is between a first reference value and a second reference value, and increasing cranking torque of the MHSG when the moving average value of the aging factor is between the first reference value and the second reference value.