Gamma-ray bursts (GRBs), have been widely used as distance indicators to measure the cosmic expansion and explore the nature of dark energy. A popular method adopted in previous works is to calibrate the luminosity relations which are responsible for distance estimation of GRBs with more primary (low redshift) cosmic distance ladder objects, type Ia supernovae (SNe Ia). Since distances of SNe Ia in all SN Ia samples used to calibrate GRB luminosity relations were usually derived from the global fit in a specific cosmological model, the distance of GRB at a given redshift calibrated with matching SNe Ia was still cosmological-model-dependent. In this paper, we first directly determine the distances of SNe Ia with the Angular Diameter Distances (ADDs) of galaxy clusters without any assumption for the background of the universe, and then calibrate GRB luminosity relations with our cosmology-independent distances of SNe Ia. The results suggest that, compared to the previous original manner where distances of SNe Ia used as calibrators are determined from the global fit in a particular cosmological model, our treatments proposed here yield almost the same calibrations of GRB luminosity relations and the cosmological implications of them do not suffer any circularity.