The exact relationship between the long gamma-ray burst (LGRB) rate and the cosmic star formation rate (CSFR) is essential for using LGRBs as cosmological probes. In this work, we collect a large sample composed of 371 Swift LGRBs with known redshifts and prompt emission properties. We first compare the rest-frame prompt properties of these bursts in different redshift bins, finding negligible redshift evolution of the luminosity of LGRBs with L_iso_>~10^51^erg/s between z~1 and z~4. Then, by utilizing the CSFR obtained from the large-scale cosmological hydrodynamical simulation, the Illustris simulation, we calculate the cumulative redshift distribution of LGRBs under different metallicity thresholds. After comparing with our sample, we find that the predictions with a moderate threshold between 0.3Z_{sun}<=Z_th<=1.0Z_{sun}_ are consistent with the sample between redshift 0