An engine fuel system includes a fuel delivery system including a first fuel pump that is coupled to a pressure relief valve that is arranged in parallel with a second fuel pump. The first fuel pump is disposed to deliver pressurized fuel to the second fuel pump and the pressure relief valve, and the second fuel pump is disposed to deliver pressurized fuel to the fuel rail. A controller characterizes the first fuel pump to determine a relationship between a fuel pump speed and a fuel pump current at a setpoint pressure for the pressure relief valve. A feed-forward pump speed command is determined based upon a target fuel pressure and a fuel flowrate. A closed-loop pump speed is commanded based upon the characterization of the fuel pump. The first fuel pump is controlled to deliver fuel to the second fuel pump based thereon.