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The article considers a spatial controlled heliocentric Earth-Mars flight of a spacecraft with an imperfectly reflecting solar sail. A new mathematical model of motion is described taking into account the dynamics of motion relative to the center of mass under the forces and moments from light pressure. A spacecraft control algorithm for implementing the flight is formed on the basis of the laws of locally optimal control for the fastest change of osculating elements. The orientation of the solar sail is controlled using thin-film control elements located around the perimeter of the solar sail surface. As a result of motion simulation, the duration and trajectory of the flight, the control program and the necessary design parameters of a spacecraft with a solar sail are determined.