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In order to analyze the effects of specific speed ns of impeller pumps on hydraulic performance theoretically, relative head-flow equation and shaft powe-flow equation were deduced under the ideal fluid condition based on the basic equation of impeller pumps. The relations between the equations and ns were analyzed as well as the equations application. The results showed that the equations of relative characteristic curves of impeller pumps were functional set of high efficient operation relevant to ns and the slope of iso-efficiency curve (IeC) passing the nominal operation point (NOP). The characteristic curve describing the relation of relative head to relative capacity (RC) was the quadratic parabola of ns and the curve describing the relation of relative shaft power to RC is the cubic parabola of ns; for the RC unequal 1, pump efficiency is decreasing with increased ns. A high ns causes gentle slope of IeC passing NOP, consequent on the high efficient operation range of impeller pump approaching the capacity axis in the comprehensive characteristic curves charts; conversely, the high efficient operation range approaching the head axis for a low ns.