Tycho Brahe's model of the solar system had the earth motionless and fixed at the center with the sun and stars moving around the earth, but he incorporated Copernicus' heliocentric model so that the other, non-Earth planets orbited around the sun. Brahe admired Copernicus' work and how it could explain the observed motion of planets, but he did not agree that the earth moved.
In 2 AD, Ptolemy developed a model of the solar system that had the earth at the center and the sun, planets and stars moving around the earth. Most observations seemed to validate this model, except for observations of the planets. Mars, in particular, could be observed to "wander," moving backward and then forward again at various points. Ptolemy and others tried to address the issue with epicycles, positing that Mars was in orbit around the earth but also in another smaller orbit around itself. The epicycles didn't work well mathematically, ultimately leading to Copernicus and his model with the sun at the center and the earth in orbit around it.
Tycho Brahe, who had developed very accurate instruments to measure planetary motion, did not believe the earth could also be in motion. His data suggested that the sun and stars orbited the earth, but like many others he found Ptolemy's epicycles problematic. By incorporating Copernicus' model of the planets orbiting the sun he felt he had addressed the mathematical issues surrounding epicycles while preserving the widely held belief that the earth was at the center of the solar system, and that all the heavenly bodies revolved around it.