We determine [Formula Presented] boundary improvement coefficients up to the 1-loop level for the Schrödinger functional coupling with improved gauge actions including plaquette and rectangle loops. These coefficients are required to implement 1-loop [Formula Presented] improvement in full QCD simulations for the coupling with the improved gauge actions. To this order, lattice artifacts of the step scaling function for each improved gauge action are also investigated. In addition, passing through the Schrödinger functional scheme, we estimate more accurately the ratio of the [Formula Presented] parameters between the improved gauge actions and the plaquette action. © 2003 The American Physical Society.