We use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the E iso − E p correlation (log E iso = a + b log E p ), where E iso is the isotropic-equivalent gamma-ray energy and E p is the spectral peak energy. We update 42 long GRBs and attempt to constrain the cosmological parameters. The full sample contains 151 long GRBs with redshifts from 0.0331 to 8.2. The first method is the simultaneous fitting method. We take the extrinsic scatter σ ext into account and assign it to the parameter E iso . The best-fitting values are a = 49.15 ± 0.26, b = 1.42 ± 0.11, σ ext = 0.34 ± 0.03 and Ω m = 0.79 in the flat ΛCDM model. The constraint on Ω m is 0.55 < Ω m < 1 at the 1σ confidence level. If reduced χ 2 method is used, the best-fit results are a = 48.96 ± 0.18, b = 1.52 ± 0.08, and Ω m = 0.50 ± 0.12. The second method uses type Ia supernovae (SNe Ia) to calibrate the E iso − E p correlation. We calibrate 90 high-redshift GRBs in the redshift range from 1.44 to 8.1. The cosmological constraints from these 90 GRBs are Ω m = 0.23 +0.06 −0.04 for flat ΛCDM and Ω m = 0.18 ± 0.11 and Ω Λ = 0.46 ± 0.51 for non-flat ΛCDM. For the combination of GRB and SNe Ia sample, we obtain Ω m = 0.271 ± 0.019 and h = 0.701 ± 0.002 for the flat ΛCDM and the non-flat ΛCDM, and the results are Ω m = 0.225 ± 0.044, Ω Λ = 0.640 ± 0.082, and h = 0.698 ± 0.004. These results from calibrated GRBs are consistent with that of SNe Ia. Meanwhile, the combined data can improve cosmological constraints significantly, compared to SNe Ia alone. Our results show that the E iso − E p correlation is promising to probe the high-redshift Universe.