We study the phase behavior, the characteristic times, and the rheological properties under the steady shear flow of the mixtures consisting of telechelic and monofunctional associating polymers by a coarse-grained molecular dynamics simulation. The mixtures form the transient networks, the closely packed spherical micelles, and the wormlike micelles. We confirm the molecular origins of the several characteristic times of the mixtures. The dependencies of the characteristic times on the composition ratio between telechelic and monofunctional associating polymers show good agreement with reported experimental results. Under the steady shear flow, the mixtures show the shear thinning induced by the change of the spatial configuration of the micelles. The telechelic associating polymers especially play an important role in connecting the micelles at the shear thinning regime and enhance the steady shear viscosity. Furthermore, at the wormlike micellar region, the mixtures show the second shear thinning initiated by the transformation of the association conformation of the telechelic associating polymers.