The author considers iterated function systems with place-dependent probabilities. Under some conditions including average contractivity, Hölder-continuity of the place dependent probabilities and a lower bound for distance divergence they establish geometric convergence of the transition probabilities to a unique invariant measure of the corresponding Markov chain. This extends a result in [S. T. Rachev and L. Rüschendorf, Mass transportation problems. Vol. 2: Applications. New York, NY: Springer (1998; Zbl 0990.60500)] as well as in [A. Lasota, Lect. Notes Phys. 457, 235–255 (1995; Zbl 0835.60058)] and [T. Szarek, Stud. Math. 154, No. 3, 207–222 (2003; Zbl 1036.47003); Diss. Math. 415, 1–62 (2003; Zbl 1051.37005)] for the place independent case. The proof is based on a classical coupling technique for the total variation distance.