Detailed atmospheric characterization of exoplanets by transmission spectroscopy requires careful consideration of stellar surface inhomogeneities induced by star-spots. This effect is particularly problematic for planetary systems around M-dwarfs, and their spot properties are not fully understood. We investigated the stellar activity of the young M-dwarf K2-25 and its effect on transit observations of the sub-Neptune K2-25 b. From multiband monitoring observations of stellar brightness variability using ground-based telescopes and Transiting Exoplanets Survey Satellite, we found that the temperature difference between the spots and photosphere is <190 K and the spot covering fraction is <61 per cent (2σ). We also investigated the effect of starspot activity using multiepoch, multiband transit observations. We rule out cases with extremely low spot temperatures and large spot covering fractions. The results suggest that spots could distort the transmission spectrum of K2-25 b by as much as ~100 ppm amplitude, corresponding to the precision of JWST/NIRSPEC of the target. Our study demonstrates that simultaneous multiband observations with current instruments can constrain the spot properties of M-dwarfs with good enough precision to support atmospheric studies of young M-dwarf planets via transmission spectroscopy.