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A new constitutive creep model for Ni-base superalloys has been developed that links the instantaneous creep response to incremental microstructure changes occurring during creep. The structure starts with cuboidal γ′- particles embedded in the γ-phase, and transitions to a rafted structure. In the present Kocks-Mecking type of model, the dislocation density ρ is considered as a state variable that evolves during creep. The increase of ρ depends on the γ-channel width in the γ/γ′-microstructure. Recovery, i.e., the reduction of ρ, is modelled from thermally activated, mechanically assisted climb. The strain rate is also modelled from the very same recovery process. The model successfully describes creep curves in a range of temperatures and load stresses with a maximum of five physical parameters. Once the model has been calibrated, it can be used to predict creep curves for other temperatures, stresses, and microstructures if the channel width evolution is known. The model is even capable of making reasonable predictions when fitted only to a single experiment. Extrapolations to different alloys with moderately varying compositions are possible.