In an oil pump structure of an automatic transmission using a torque converter, a hydraulic pressure chamber is defined by a pump housing and a pump cover, to rotatably accommodate therein inner and outer rotors. First and second inflow ports respectively communicating with an oil strainer and a control valve are formed in the outside surface of the pump cover separately from each other. First and second oil inflow passages communicating with the respective inflow ports, a merged-flow portion that downstream portions of the first and second oil inflow passages are merged with each other, a downstream-side oil distribution channel intercommunicating a downstream side of the merged-flow portion and the hydraulic pressure chamber, are formed in at least one of the pump housing and the pump cover.