The paper considers the task of simulation quadcopter motion control in vir-tual environment systems. The proposed solution of this task is based on the application of a mathematical model of quadcopter dynamics, in which quaternion and axis-angle representation of the attitude are used. In this work, a feedback linearization method for the equations of quadcopter and its elec-tric motors dynamics is proposed to control the quadcopter. With the application of this approach, quadcopter motion is achieved by the obtained expressions for linear acceleration and the desired quaternion. The proposed methods and approaches for quadcopter simulation were implemented in the software package of virtual environment and tested using examples of the motion of a quadcopter model along a given path.