By using a formalism based on quantum transport equation, we study the current response of an electron gas strongly coupled to an intense terahertz laser. The effect of laser is treated exactly, which gives rise to the electron-photon sidebands. Our formalism includes up to the second order in electron-impurity scattering and to any order in optical transitions between the sidebands. Resonant scattering can occur when the frequency of the probing field equals a multiple of the terahertz laser frequency. The usual linear response theory is the zero-photon term in our formalism. This result can be applied to study the electrical transport in strongly coupled electron-photon systems. One such system is a two-dimensional semiconductor structure under an intense terahertz radiation.