An algorithm of forecasting of the ionosphere F2 layer critical frequency for time intervals: 1, 2, 3, 12, and 24 hours was developed on the basis of the technology of artificial neural networks (ANN). The experimental search for a valid training array and architecture of ANN was performed. The solar wind parameters, interplanetary magnetic field, and geomagnetic disturbance indexes were additionally used in the forecasting. This made it possible to improve its effectiveness. The practical importance of the performed work is in the application of its results for efficient correction of the ionosphere model for an improvement of the ionosphere shortwave radio communication.