In this paper, we study random walks on a finitely generated group G which has a free action on a Zn-tree. We show that if G is non-abelian and acts minimally, freely and without inversions on a locally finite Zn-tree Γ with the set of open ends Ends(Γ), then for every non-degenerate probability measure μ on G there exists a unique μ-stationary probability measure νμ on Ends(Γ), and the space (Ends(Γ),νμ) is a μ-boundary. Moreover, if μ has finite first moment with respect to the word metric on G (induced by a finite generating set), then the measure space (Ends(Γ),ν_μ) is isomorphic to the Poisson–Furstenberg boundary of (G, μ).