Over the past decades, the automotive industry has made significant efforts to improve engine fuel economy by reducing mechanical friction. Reducing friction under cold conditions is becoming more important in hybrid vehicle (HV) and plug-in hybrid vehicle (PHV) systems due to the lower oil temperatures of these systems, which results in higher friction loss. To help resolve this issue, a new internal gear fully variable discharge oil pump (F-VDOP) was developed. This new oil pump can control the oil pressure freely over a temperature range from -10°C to hot conditions. At 20°C, this pump lowers the minimum main gallery pressure to 100 kPa, thereby achieving a friction reduction effect of 1.4 Nm. The developed oil pump achieves a pressure response time constant of 0.17 seconds when changing the oil pressure from 120 kPa to 200 kPa at a temperature of 20°C and an engine speed of 1,600 rpm. Test results confirmed that the developed oil pump controlled the oil pressure with an undershoot of about 12%. The oil jets were also stopped from -10°C. The internal gear tooth profile was also improved and reduced the friction of the rotor by 34% compared to a conventional trochoidal tooth profile. This paper describes the details of the design of the new internal gear rotor, the structure of the new F-VDOP, the engine oil circuit, and the test results. This new oil pump improves fuel economy by 1.2% under the LA#4 cold test cycle.