In this paper, an electric oil pump control algorithm for an automatic-transmission-based hybrid electric vehicle was proposed. Dynamic models of the hybrid electric vehicle powertrain and hydraulic control system, including a mechanical oil pump and an electric oil pump, were obtained, and a hybrid electric vehicle performance simulator was developed. Also, a flow consumption model of the hydraulic control system was constructed. To represent the characteristics of the hydraulic control system according to the change in the temperature of the automatic transmission fluid, a viscosity index concept was introduced. Based on the simulation and test results, a viscosity index-line pressure-electric oil pump power map was proposed to describe the power supply requirement according to the viscosity index and the required line pressure. Using the viscosity index-line pressure-electric oil pump power map, an electric oil pump control algorithm was suggested to control the electric oil pump by using multi-stage power for a given viscosity index. The mechanical oil pump speed at which the electric oil pump is turned off was obtained on the basis of the flow consumption model. The electric oil pump control algorithm was evaluated by experiments and simulations. The proposed electric oil pump control algorithm satisfied the target line pressure requirement according to the viscosity index. In addition, an electric oil pump control strategy during an automatic transmission gear shift was suggested for the situation in which the maximum line pressure required for the gear shift cannot be achieved by only the mechanical oil pump. The electricoil-pump-assisted power was determined from the flow consumption model and the mechanical oil pump speed considering the gear shift. The simulation results confirmed that the electric oil pump control strategy satisfied the maximum line pressure during a gear shift.