Introduction. The higher education system is being modernized at the Master’s level according to the requirements of the Federal State Educational Standards 3++. Teaching English to non-English major students shows that the intensive use of electronic learning tools requires the development of a system of tasks for effective language training. The purpose of the article is to develop a system of tasks for the developing EFL graduates’ communicative competence and to prove its effectiveness in teaching practice. Materials and methods. The pilot training was conducted at the North-Eastern Federal University named after M. K. Ammosov (N=90) and the Arctic State University of Agriculture and Technology (N=60) during one academic year. Classes were conducted both in full-time and remotely using the Zoom platform and the virtual learning environment Moodle. The entrance and final diagnostics were conducted in all four English skills (listening, speaking, reading and writing) to determine the level of EFL communicative competence in Master’s students. Results of the study. The obtained results of the diagnostic stage determined the directions of training in order to improve students’ EFL communicative competence: 1) modernization of the language education (updating the English course content); 2) development of a system of tasks for the organizing distance learning (updating of the educational and methodological complex). The results of the final testing indicate an increase in the level of EFL communicative competence at the end of the pilot training: 1) the average value for listening, speaking and writing increased by 1.5 times at the significance level p≤0.01; 2) the average value for reading increased by 2.5 times at the significance level p≤0.01.