To meet the requirements of fuel pumps with high efficiency, high power density, and low flow ripple for modern advanced aircraft, we hereby propose a two-dimensional piston pump (called 2D pump). A single piston with both rotary and linear motions is used to combine the flow distributing and volumetric varying functions together. The leakage spots are reduced to the clearance between the piston and the cylinder. As the radial force of the piston is balanced, a small piston clearance is selected to reduce leakage. Furthermore, a 2D tandem pump formed by two 2D pump units connected in series was introduced to eliminate the geometric flow ripple. The flow ripple characteristics were studied through analytical techniques, CFD numerical methods, and experiments. The results show that the flow ripple of 2D pump obtained by the measured pressure wave is 6.3%, while the pump has a high volumetric efficiency of up to 96% within a speed range of 1000-8000 r/min, indicating that reducing the leakage increases the average actual flow and reduces the flow ripple. Therefore, the proposed 2D pump is suitable for modern advanced aircraft.