We present the real time formalism of the functional renormalization group method for the 3-dimensional $\phi^4$ theory. The original, single time formalism of the renormalization is based on the invariance of the transition amplitudes. By using the so-called closed time path formalism we will deduce the real time RG equations based on the invariance of the physically more relevant expectation values. In the case of zero temperature the phase space does not change qualitatively when we compare it by the ones obtained by the original RG treatment. The real time formalism enables us to take into account the finite temperature version of the $\phi^4$ theory in a simple manner. The evolution of the mixing couplings can account for the decoherence in the model.