In the gravity quantum theory, the quantization of spacetime may lead to the modification of the dispersion relation between the energy and the momentum and the Lorentz invariance violation (LIV). High energy and long-distance gamma-ray burst (GRB) observations in the Universe provide a unique opportunity to test the possibility of LIV. In this work, we use 88 time delays from GRBs ($0.117<z<6.29$), and provide a cosmological model-independent approach based on the luminosity distance data from 174 GRBs to test LIV. Combining the observation data from a multiband of GRBs provides us with an opportunity to mitigate the potential systematic errors arising from variations in the physical characteristics among diverse object populations, and to add a higher redshift dataset for testing the energy-dependent velocity caused by the corrected dispersion relationship of photons. These robust limits of the energy scale for the linear and quadratic LIV effects are $E_{\mathrm{QG},1}\ge 1.5\times {10}^{15}\mathrm{GeV}$, and $E_{\mathrm{QG},2}\ge 8.5\times {10}^9\mathrm{GeV}$, respectively. It exhibits a significantly reduced value compared to the energy scale of Planck in both scenarios of linear and quadratic LIV.

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• Cosmology
• Gamma ray astronomy
• Gamma ray bursts
• Quantum gravity