As the importance of transmission efficiency to reducing fuel consumption and conserving the environment rapidly increases, reducing the drag torque in an automotive wet clutch is emerging as an important issue in the automotive industry. The drag torque in a clutch occurs from viscous drag generated by automatic transmission fluid in the narrow gap between separate friction plates. In this study, the drag torques in an automotive wet clutch are investigated with respect to the angle and density of the grooves between separate friction plates by three-dimensional finite element simulation of a single set of wet clutch disks considering the two-phase flow of air and oil. The simulation results shows that the drag torque generally increases with the rotational speed to a critical point and then decreases at the high-speed regime. The grooves between the plates plays an important role in reducing the drag peak, and the inclined angle of the grooves affects the oil flow. The grooves with an angle of $50^{circ}$ shows the lowest drag torques at both low and high speeds. The flow vectors inside the $50^{circ}$ grooves shows clear evidence that the fluid flows out more easily from the grooves compared with the flow vectors inside grooves with lower angles. The simulation results shows that increasing the number of grooves (density of grooves) decreases the drag torque.