A modified version of Sverre Aarseth's GPU-enabled direct N-body code NBODY6 has been developed which includes the effects of dynamical friction on a star cluster in a semi-analytical way, as a fast approximate method of modelling star cluster inspiral in a background distribution of stars. In this approach the background potential is completely analytic, whilst a perturbative term reproduces the effects of dynamical friction using properties of both the cluster and the background at the current epoch. Using this approach only the cluster particles need to be modeled in an N-body fashion, greatly decreasing computation time. The code is compared with fully self-consistent models comprised of granular background distributions computed with NBODY6 and the tree-code GADGET, showing good agreement. The code could be useful for other N-body models in which dynamical friction is important. The code will be released publicly.