In order to resolve the constant pressure and flow output problems of reciprocating pump, a kind of hydraulic pump with double-cylinder and single acting was designed. Hydraulic system of the pump is made up of 2 hydraulic pumps. The oil is supplied to the hydraulic system using double oil pump with oil mass distribution mode combining a unidirectional mechanism turning valve and an ordinary turning valve. The action of turning valve is controlled by the piston strokes and the action precision of valve is not under the influence of the changing of main hydraulic pump displacement. The system is controlled reliably with good result in practical application.