There have been no obvious design criteria of high efficient displacement pump using a dimensionless parameter which can represent many physical aspect of displacement pump could be very useful to estimate displacement pump performance. Many dimensionless analysis methods have been developed in fluid dynamics, machine design and so on. In this study a new dimensionless parameter is developed for estimate displacement pump performance and efficiency, until now to evaluate the performance of displacement pumps which are widely used in industry field, primarily experimental methods have been used. The dimensionless parameter contains many physical information about pump design. For example, they are the relation between flow rate and power, displacement operation displacement and size, inlet and outlet valve size. And the developed dimensionless functions are induced from numerical method.