A modified multiscale method without constitutive equation is proposed to investigate the microscopic information and macroscopic flow properties of polymeric fluid with the memory effect between parallel plates. In this method, the domain is entirely described by macro model with isolated molecular dynamics simulations applied to calculate the necessary local stresses. The present method is firstly verified by the creep-recovery motion and pressure-driven flow, and all results are in excellent agreement with the available numerical solutions in literature. Then, the method is extended to simulate two typical problems of relatively large spatial scale in general beyond the capability of molecular dynamics simulations. In the planar Couette flow, the relationship between macroscopic properties and the time evolution of local molecular information is investigated in detail without long time averaging. All results which are consistent with nonequilibrium molecular dynamics and literature qualitatively or quantitatively demonstrate the validity of present multiscale method in simulating transient viscoelastic flows and the capacity to obtain the polymer information. In the pressure-driven flow, a general monotonically decreasing relationship between the maximum or average velocities and the polymer concentrations has been found regardless of the polymer chain length. Particularly, the reference concentration which satisfies a power law with chain length is closely related to the overlap concentration, and the reference velocity is exactly the relevant velocity of Newtonian fluid with corresponding zero shear rate viscosity.