The increasingly deep limit on the neutrino emission from gamma-ray bursts ( GRBs ) with IceCube observations has reached the level that could put useful constraints on the fireball properties . We first present a revised analytic calculation of the neutrino flux , which predicts a flux an order of magnitude lower than that obtained by the IceCube collaboration . For benchmark model parameters ( e.g . the bulk Lorentz factor is \Gamma = 10 ^ { 2.5 } , the observed variability time for long GRBs is t _ { v } ^ { ob } = 0.01 { s } and the ratio between the energy in accelerated protons and in radiation is \eta _ { p } = 10 for every burst ) in the standard internal shock scenario , the predicted neutrino flux from 215 bursts during the period of the 40-string and 59-string configurations is found to be a factor of \sim 3 below the IceCube sensitivity . However , if we accept the recently found inherent relation between the bulk Lorentz factor and burst energy , the expected neutrino flux increases significantly and the spectral peak shifts to lower energy . In this case , the non-detection then implies that the baryon loading ratio should be \eta _ { p } \lesssim 10 if the variability time of long GRBs is fixed to t _ { v } ^ { ob } = 0.01 { s } . Instead , if we relax the standard internal shock scenario but keep to assume \eta _ { p } = 10 , the non-detection constrains the dissipation radius to be R \gtrsim 4 \times 10 ^ { 12 } { cm } assuming the same dissipation radius for every burst and benchmark parameters for fireballs . We also calculate the diffuse neutrino flux from GRBs for different luminosity functions existing in the literature . The expected flux exceeds the current IceCube limit for some luminosity functions , and thus the non-detection constrains \eta _ { p } \lesssim 10 in such cases when the variability time of long GRBs is fixed to t _ { v } ^ { ob } = 0.01 { s } .