We employed the nonequilibrium dissipative particle dynamics method to study the shear flow behaviors of rod-coil diblock copolymers in solutions. The effects of copolymer concentrations and molecular architecture on the rheology are investigated. The simulated results show that the shear flow behaviors change from Newtonian to non-Newtonian when the morphologies transform from micelles to gels by increasing the copolymer concentrations. For the non-Newtonian systems, it was found that the curve of the viscosity versus shear rate is divided into three regions, that is, shear thinning region I, platform region II, and shear thinning region III. From the physical origin, the three-region behavior is governed by the distinct flow behaviors of the rod and coil blocks and their different time scale in response to the shear field. Additionally, by tuning the molecular architectures, the simulated results reveal that the slopes in region I and region III are influenced by the length of rod and coil blocks, respectively. The present research revealed the microscopic origin of the complex rheological properties of rod-coil diblock copolymers in solutions and could provide useful information for preparing functional materials based on block copolymers.

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