In this study, we attempted to develop a model to describe a pointing task in a three-dimensional environment, particularly in a car cockpit. When humans interact with a system in three-dimensional space, they usually reach toward targets to adjust controls. Hence, reaching movements are considered to describe pointing tasks in three-dimensions. However, the ACT-R cognitive architecture deals only with two-dimensions with hand movements using Fitts' law or parameters. Therefore, this paper proposes a method to describe the reaching arm movement of a person in a three-dimensional environment by extending the motor module of ACT-R. Arm movement is more complicated bio-logically than hand movement, because many aspects such as kinematic features have to be considered. In this study, an extended Fitts' law that includes the azimuth angle and inclination angle was used to develop the extended motor module to represent human reaching actions. A pointing task was then simulated using an extended ACT-R in a mock-up vehicle. The extended motor module was found to simulate pointing movements in three-dimensional environments accurately with an r-squared value of 0.947. In addition, the extended motor module is able to describe the variations in movement determined by the targets' locations and directions.