The aim of the current work is to describe a new model for flows in translational non-equilibrium. Starting from the statistical description of gas proposed by Boltzmann, the model relies on a domain decomposition technique in the velocity space. Using the maximum entropy principle, the logarithm of the distribution function in each velocity subdomain (group) is expressed with a power series in molecular velocity. New governing equations are obtained using method of weighted residuals by taking the velocity moments of the Boltzmann's Equations. The model is applied to a spatially homogeneous Boltzmann Equation with a Bhatnagar-Gross-Krook1(BGK) model collision operator and the relaxation of the initial non-equilibrium distribution to a Maxwellian is studied using the model. In addition, the numerical results obtained using the model for a 1D shock tube problem are also reported.