Dual-phase high-entropy alloys (DP-HEAs) have been proved to be a kind of promising materials that exhibit a combination of excellent strength and ductility. Previous studies have emphasized the effect of interface and phase volume fraction on mechanical performance in DP-HEAs. However, the deformation mechanisms such as interplays between dislocations and the constituent phases have not been fully understood. Particularly, the research concerning plastic anisotropy in DP-HEAs is still lacking. Here, molecular dynamics simulations are performed to probe the effect of loading orientation on plasticity in the nano-laminated face-centered cubic (FCC)/hexagonal close-packed (HCP) CoNiCrFeMn DP-HEA. Results reveal that a switch from strengthening to softening and back to strengthening is closely related to the activation of different slip systems when tailoring the inclination angles of the nanolaminates with respect to the tensile direction from 0° to 90°. Slip transfer across phase boundaries, phase transformation and the nucleation of shear bands dominate the plasticity in the samples with low, medium and high inclination angles, respectively. Furthermore, the evolution of microstructures, such as dislocations, stacking faults, and FCC/HCP phase are analyzed to study the underlying deformation mechanisms. These results can help understand the plastic anisotropy of DP-HEAs and design alloys with excellent mechanical properties for engineering applications.