Let OΛ be a higher-rank graph C*-algebra. For every p in Z+r there is a canonical completely positive map Φp on OΛ and a subshift Tp on the path space X=Λ∞. We show that ht(Φp)=h(Tp), where ht is Voiculescu's approximation entropy and h the classical topological entropy. For a higher rank Cuntz-Krieger algebra OM we obtain ht(Φp)= log rad(M1 p1... Mr pr), rad being the spectral radius. This generalizes Boca and Goldstein's result for Cuntz-Krieger algebras.