  We determine O($a$) boundary improvement coefficients up to 1-loop level for
the Schr\"odinger Functional coupling with improved gauge actions including
plaquette and rectangle loops. These coefficients are required to implement
1-loop O($a$) improvement in full QCD simulations for the coupling with the
improved gauge actions. To this order, lattice artifacts of step scaling
function for each improved gauge action are also investigated. In addition,
passing through the SF scheme, we estimate the ratio of $\Lambda$-parameters
between the improved gauge actions and the plaquette action more accurately.
