Type Ia Supernovae (SNe Ia) are widely used to measure distances in the Universe. Despite the recent progress achieved in SN Ia standardization, the Hubble diagram still shows some remaining intrinsic dispersion. The remaining scatter in supernova luminosity could be due to the environmental effects that are accounted for as mass step correction in the current cosmological analyses. In this work, we compare the local and global colour (U − V), the local star formation rate, and the host stellar mass to the host galaxy morphology. The observed trends suggest that the host galaxy morphology is a relevant parameter to characterize the SN Ia environment. Therefore, we study the influence of host galaxy morphology on light-curve parameters of SNe Ia from the pantheon cosmological supernova sample. We determine the Hubble morphological type of host galaxies for a subsample of 330 SNe Ia. We confirm that the salt2 stretch parameter x_1 depends on the host morphology with the p-value ∼10^−14. The supernovae with lower stretch value are hosted mainly by elliptical and lenticular galaxies. No correlation for the salt2 colour parameter c is found. We also examine Hubble diagram residuals for supernovae hosted by ‘early-type’ and ‘late-type’ morphological groups of galaxies. The analysis reveals that the mean distance modulus residual in early-type galaxies is smaller than the one in late-type galaxies, which means that early-type galaxies contain brighter supernovae after stretch and colour corrections. However, we do not observe any difference in the residual dispersion for these two morphological groups. The obtained results are in the line with other analyses showing environmental dependence of SN Ia light-curve parameters and luminosity. We confirm the importance of including a host galaxy parameter into the standardization procedure of SNe Ia for further cosmological studies.