Strong X-ray and γ–ray flares have been detected in February 2010 from the high synchrotron peaked blazar Mrk 421 (z = 0.031). With the motivation of understanding the physics involved in this flaring activity, we study the variability of the source in X-ray and γ–ray energy bands during the period February 10–23, 2010 (MJD 55237–55250). We use near simultaneous X-ray data collected by MAXI, Swift -XRT and γ–ray data collected by Fermi -LAT and TACTIC along with the optical V-band observations by SPOL at Steward Observatory. We observe that the variation in the one day averaged flux from the source during the flare is characterized by fast rise and slow decay. Besides, the TeV γ–ray flux shows a strong correlation with the X-ray flux, suggesting the former to be an outcome of synchrotron self Compton emission process. To model the observed X-ray and γ–ray light curves, we numerically solve the kinetic equation describing the evolution of particle distribution in the emission region. The injection of particle distribution into the emission region, from the putative acceleration region, is assumed to be a time de- pendent power law. The synchrotron and synchrotron self Compton emission from the evolving particle distribution in the emission region are used to reproduce the X-ray and γ–ray flares successfully. Our study suggests that the flaring activity of Mrk 421 can be an outcome of an efficient acceleration process associated with the increase in underlying non-thermal particle distribution.