The paper presents control algorithm of quadcopter dynamics under the influence of perturbations, described by step functions. The aim of this work is to develop the control law of quadcopter dynamics, providing stabilization and astaticism of regulated variables on the base of the so-called speed controller. Speed controller was proposed in the papers of Veremey E.I. as one of the elements of controller with a special multi-purpose structure, which is described by linear time-invariant system and allows having stability of regulated variables and also the required dynamic properties in the presence of external perturbations. Such controllers can be effectively used in a number of control tasks for dynamic objects, in particular, they are actively used for marine mobile objects control. The mathematical model of quadcopter is described, for which the regulated variables control is constructed on the base of simplified linear models. For each of simplified models the speed controller is designed, which due to its structural features can suppress the action of the step disturbances. Usually, this property is provided by introducing the integral components for regulated variables in the control law. To demonstrate the efficiency of the algorithm, some graphical illustrations of transient processes in height, heading, roll and pitch, obtained as a result of simulation in MATLABSimulink, are given in the work.