We model the simultaneous observations of the flat-spectrum radio quasar 3C 279 at radio, optical, X-ray and very high energy (VHE) gamma-ray energies during 2006 flare using a simple one-zone leptonic model. We consider synchrotron emission due to cooling of a non-thermal electron distribution in an equipartition magnetic field and inverse Compton emission due to the scattering of synchrotron photons (SSC) and external soft photons (EC) by the same distribution of electrons. We show that the VHE gamma-ray flux cannot be explained by an SSC process thereby suggesting the EC mechanism as a plausible emission process at this energy. The EC scattering of broad-line region photons to very high energies will be in the Klein–Nishina regime predicting a steep spectrum which is contrary to the observations. However, the infrared photons from the dusty torus can be boosted to very high energies with the scattering process remaining in the Thomson regime. Though the EC process can successfully explain the observed VHE flux, it requires a magnetic field much lower than the equipartition value to reproduce the observed X-ray flux. Hence, we attribute the X-ray emission to the SSC process. We derive the physical parameters of 3C 279 considering the above-mentioned emission processes. In addition, we assume the size of the emission region constrained by a variability time-scale of one day. This model can successfully reproduce the broad-band spectrum of 3C 279 but predicts substantially large flux at MeV–GeV energies.