An adaptive engine speed control system for a grass mowing machine having an internal combustion engine, a hydrostatic traction drive circuit and a hydraulic mowing circuit for operating a plurality of cutting units. A controller provides a traction feedback output signal if the grass mowing machine is moving at an actual ground speed that is below a pedal based desired ground speed, and uses the traction feedback output signal to command the internal combustion engine to an increased speed above a pedal based engine speed control range.