Gamma-ray bursts (GRBs) being the most luminous among known cosmic objects carry an essential potential for cosmological studies if properly used as standard candles. In this paper we test with GRBs the cosmological predictions of the Gurzadyan-Xue (GX) model of dark energy, a novel theory that predicts, without any free parameters, the current vacuum fluctuation energy density close to the value inferred from the SNIa observations. We also compare the GX results with those predicted by the concordance scenario $Λ$-CDM. According to the statistical approach by Schaefer (2007), the use of several empirical relations obtained from GRBs observables, after a consistent calibration for a specific model, enables one to probe current cosmological models. Based on this recently introduced method, we use the 69 GRBs sample collected by Schaefer (2007); and the most recently released SWIFT satellite data (Sakamoto et al. 2007) together with the 41 GRBs sample collected by Rizzuto et al. (2007), which has the more firmly determined redshifts. Both data samples span a distance scale up to redshift about 7. We show that the GX models are compatible with the Hubble diagram of the Schaefer (2007) 69 GRBs sample. Such adjustment is almost identical to the one for the concordance $Λ$-CDM. ; Comment: 9 pages, 17 figures, 11 tables; Astr. & Astrophys. (in press)