A matrix-based calculation for the electron velocity distribution function (EVDF) in gas under dc electric field is demonstrated. The propagator matrix power method (PMPM) repeats squaring the propagator matrix P for its powers P 2, P 4, P 8, P 16, ⋯, up to a sufficient order of the power P 2 S . P is a square matrix representing the change of EVDF due to the electron acceleration by an electric field and the electron scattering by gas molecules in a time step Δt. With an initial EVDF f(t 0) in a form of a column vector, a matrix product P 2 S f ( t 0 ) gives the EVDF at t = t 0 + 2 S Δt. The PMPM enables us to observe the EVDF relaxation in a logarithmic time scale with a linear increase of the matrix squaring steps S. Features of the PMPM are discussed, and theoretically possible extensions to models under crossed electric and magnetic fields and ac electric field are investigated.