  We present results for the equation of state for pure SU(3) gauge theory
obtained with a renormalization-group (RG) improved action. The energy density
and pressure are calculated on a $16^3\times 4$ and a $32^3\times 8$ lattice
employing the integral method. Extrapolating the results to the continuum
limit, we find the energy density and pressure to be in good agreement with
those obtained with the standard plaquette action within the error of 3-4%.
