The article analyzes the method of developed author program for teaching gifted students the English communication, changing of the form of conducting lessons, taking into account the phenomenon of gift and using the ICT. The teaching program of the dialogical speech for the gifted students is developed taking into account: psychological features of the gifted children, age peculiarities, nature and specificity of dialogue, as the type of speaking activity. The special attention in the research is paid to the use of modern technologies (ICT). The experimental program is based on the conceptions of communicative and cognitive method of teaching English, didactic and methodical principles of teaching. Among four basic principles of teaching English there is a communicative orientation; personality orientation; self-education; computer-integrated teaching all types of speaking activity (listening, speaking, reading and writing) and a new principle – cultural. The system of exercises included reproductive, reproductive-creative, creative (preparatory, introductory, training, finishing, control) exercises, it was orientated on realization of all types of speaking activity and based on reproductive and productive facilities of knowledge mastering and the development of abilities and skills of the dialogue speech of senior pupils. The main idea of our methodology is the use of audio-visual material in foreign language teaching because of the increasing emphasis on communicative techniques, and as it is obvious that the use of video is a great help for foreign language teachers in stimulating and facilitating the target language.