The Tychonian system was an effort by Tycho Brahe to create a model that allows for observations such as the phases of Venus within a geocentric model. In the Tychonian system, the Earth is in the center of the universe, the sun revolves around the earth and the other planets revolve around the sun. It can be shown through a geometric argument that the motions of the planets and the sun relative to the Earth in the Tychonian system are equivalent to the motions in the Copernican system, and the Tychonian system has the advantage of not predicting stellar parallax, which was not observable in the 16th century.
Ultimately the Tychonian system was rejected along with the Copernican system by the observations of Brahe himself, which were used by Johannes Kepler to demonstrate that the orbits of the planets are ellipses and not circles.
In the modern era, the few who still subscribe to geocentrism use a Tychonian system with elliptical orbits. See modern geocentrism.