A high pressure pump for complex injection engines is provided. A body of the high pressure pump includes a first flow path that transports the low pressure fuel flowing in through the low pressure fuel inlet and a low pressure fuel storage chamber that is disposed in a lower portion of the body to store the low pressure fuel transported from the first flow path. A second flow path transports the low pressure fuel stored in the low pressure fuel storage chamber and a flow control valve is disposed over the low pressure fuel storage chamber to discharge the low pressure fuel, transported through the second flow path, to the pressure unit or the damper disposed in an upper portion of the body based on an opening or closing operation. A low pressure fuel outlet discharges the low pressure fuel, transported through the damper, to a low pressure fuel rail.