This paper discusses the evolution of the correlation between galaxy star formation rates (SFRs) and stellar mass (M) over the last ∼10 Gyr, particularly focusing on its environmental dependence. We first present the mid-infrared (MIR) properties of the Hα-selected galaxies in a rich cluster Cl 0939+4713 at z = 0.4. We use wide-field Spitzer/MIPS 24 μm data to show that the optically red Hα emitters, which are most prevalent in group-scale environments, tend to have higher SFRs and higher dust extinction than the majority population of blue Ha sources. With an MIR stacking analysis, we find that the median SFR of Hα emitters is higher in higher density environment at z = 0.4. We also find that star-forming galaxies in highdensity environment tend to have higher specific SFR (SSFR), although the trend is much less significant compared to that of SFR. This increase of SSFR in high-density environment is not visible when we consider the SFR derived from Hα alone, suggesting that the dust attenuation in galaxies depends on environment; galaxies in high-density environment tend to be dustier (by up to ∼0.5 mag), probably reflecting a higher fraction of nucleated, dusty starbursts in higher density environments at z = 0.4. We then discuss the environmental dependence of the SFR-M relation for star-forming galaxies since z ∼ 2, by compiling our comparable, narrow-band-selected, large Haemitter samples in both distant cluster environments and field environments. We find that the SSFR of Hα-selected galaxies (at the fixed mass of log(M_*/M_⊙) = 10) rapidly evolves as (1 + z)³, but the SFR-M_* relation is independent of the environment since z ∼ 2, as far as we rely on the Hα-based SFRs (with M^*-dependent extinction correction). Even if we consider the possible environmental variation in the dust attenuation, we conclude that the difference in the SFR-M_* relation between cluster and field star-forming galaxies is always small (≲0.2 dex level) at any time in the history of the Universe since z ∼ 2.