There is an apparent tension between cosmological parameters obtained from Planck cosmic microwave background radiation observations and that derived from the observed magnitude-redshift relation for the type Ia supernova （SNe Ia）. Here, we show that the tension can be alleviated, if we first calibrate, with the help of the distance-duality relation, the light-curve fitting parameters in the distance estimation in SNe Ia observations with the angular diameter distance data of the galaxy clusters and then re-estimate the distances for the SNe Ia with the corrected fitting parameters. This was used to explore their cosmological implications in the context of the spatially fiat cosmology. We find a higher value for the matter density parameter, Ωm, as compared to that from the original SNLS3, which is in agreement with Planck observations at 68.3% confidence. Therefore, the tension between Planck measurements and SNe Ia observations regarding Ωm can be effectively alleviated without invoking new physics or resorting to extensions for the standard concordance model. Moreover, with the absolute magnitude of a fiducial SNe Ia, M, determined first, we obtained a constraint on the Hubble constant with SNLS3 alone, which is also consistent with Planck.
