We study the model of a driven interface in a disordered medium including the KPZ-nonlinearity. The coupled functional renormalization group flow equations for the disorder correlator and coupling constant associated with the KPZ-nonlinearity possess a strong coupling fixed-point for the interface dimensions d=1, 2. In d=1 we get the roughness exponent and the dynamical exponent in one-loop approximation respectively as ζ=0.8615 and z=1