We update gamma-ray burst (GRB) luminosity relations among certain spectral and light-curve features with 139 GRBs. The distance modulus of 82 GRBs atz>1.4can be calibrated with the sample atz≤1.4by using the cubic spline interpolation method from the Union2.1 Type Ia supernovae (SNe Ia) set. We investigate the joint constraints on the Cardassian expansion model and dark energy with 580 Union2.1 SNe Ia sample(z<1.4)and 82 calibrated GRBs’ data(1.4<z≤8.2). In ΛCDM, we find that adding 82 high-zGRBs to 580 SNe Ia significantly improves the constraint onΩm-ΩΛplane. In the Cardassian expansion model, the best fit isΩm=0.24-0.15+0.15andn=0.16-0.52+0.30 (1σ), which is consistent with the ΛCDM cosmology(n=0)in the1σconfidence region. We also discuss two dark energy models in which the equation of statew(z)is parameterized asw(z)=w0andw(z)=w0+w1z/(1+z), respectively. Based on our analysis, we see that our universe at higher redshift up toz=8.2is consistent with the concordance model within1σconfidence level.