We present the results of extensive modelling of the spectral energy distributions (SEDs) of the closest blazar (z = 0.031) Markarian 421 (Mrk 421) during a giant outburst in 2010 February. The source underwent rapid flux variations in both X-rays and very high energy (VHE) gamma rays as it evolved from a low-flux state on 2010 February 13-15 to a high-flux state on 2010 February 17. During this period, the source exhibited significant spectral hardening from X-rays to VHE gamma rays while exhibiting a 'harder when brighter' behaviour in these energy bands. We reproduce the broad-band SED using a time-dependent multizone leptonic jet model with radiation feedback.We find that an injection of the leptonic particle population with a single power-law energy distribution at shock fronts followed by energy losses in an inhomogeneous emission region is suitable for explaining the evolution of Mrk 421 from low- to high-flux state in 2010 February. The spectral states are successfully reproduced by a combination of a few key physical parameters, such as the maximum and minimum cutoffs and power-law slope of the electron injection energies, magnetic field strength, and bulk Lorentz factor of the emission region. The simulated light curves and spectral evolution of Mrk 421 during this period imply an almost linear correlation between X-ray flux at 1-10 keV energies and VHE gamma-ray flux above 200 GeV, as has been previously exhibited by this source. Through this study, a general trend that has emerged for the role of physical parameters is that, as the flare evolves from a low- to a high-flux state, higher bulk kinetic energy is injected into the system with a harder particle population and a lower magnetic field strength.