Three-dimensional discrete dislocation dynamics (DDD) simulations in combination with the phase-field method are performed to investigate the influence of different realistic Ni-base single crystal superalloy microstructures with the same volume fraction of γ′ precipitates on plastic deformation at room temperature. The phase-field method is used to generate realistic microstructures as the boundary conditions for DDD simulations in which a constant high uniaxial tensile load is applied along different crystallographic directions. In addition, the lattice mismatch between the γ and γ′ phases is taken into account as a source of internal stresses. Due to the high antiphase boundary energy and the rare formation of superdislocations, precipitate cutting is not observed in the present simulations. Therefore, the plastic deformation is mainly caused by dislocation motion in γ matrix channels. From a comparison of the macroscopic mechanical response and the dislocation evolution for different microstructures in each loading direction, we found that, for a given γ′ phase volume fraction, the optimal microstructure should possess narrow and homogeneous γ matrix channels.