The subject of the study is the formation of communication and teamwork skills of future IT-specialists, using project technology in teaching the administration of computer systems and networks. Content analysis of research has shown that communication and teamwork skills are the most requested and necessary soft skills for future IT professionals. It is offered to use project technology of training for their formation. This technology consists of the approaches and tools application used in real-world software development. To implement this technology, we propose to use mind maps for design. The organization of the working process on the project is implemented in Jira Software, Asana or Trello. Communication among project participants should be implemented with the help of several means: video chats (Zoom, Skype, Google Meet) and written communication in corporate messengers (Slack, Zulip). Experimental verification has shown the efficiency of the proposed design technology implementation.