  We investigate universality of the Nf=2 running coupling in the Sch\"odinger
functional scheme, by calculating the step scaling function in lattice QCD with
the renorm alization group (RG) improved gauge action at both weak(u=0.9796)
and strong(u=3.3340) couplings, where u=\bar{g}^2_SF with \bar{g}_SF being the
running coupling in this scheme. In our main calculations, we use the
tree-level value for O(a) improvement coefficients of boundary gauge fields. In
addition we employ the 1-loop value for them in order to see how scaling
behaviours are affected by them. In the continuum limit, the step scaling
function obtained from the RG improved gauge actions agrees with the previous
result obtained from the plaquette action within errors at both couplings,
though errors of our result are larger. Combined fits using all data with the
RG improved action as well as the plaquette action reduce errors in the
continuum limit by 2% at the weak coupling and 22% at the strong coupling.
