A two-dimensional gyroscopic phononic crystal was proposed. The unit cell of this crystal was composed of a gyroscope, an outer frame and four springs. In the unit cell, only angular motions due to gyro rotation were considered, and translations were ignored. Using the angular momentum theorem, the dynamic equation of the unit cell was established. By solving this dynamic equation, the dispersion relation was obtained and the band gap characteristic was revealed. Then, by changing the structural parameters, the variation of the band gap could be observed, and thus the influence of structural parameters on the band gap was presented. Finally, the existence of band gaps was verified by the numerical method, which showed that the 2D gyroscopic phononic crystal can effectively attenuate the torsional vibration when the frequency falls into the band gap.