In this paper, the lattice Boltzmann method is applied to simulate a dumbbell moving in a pressure-driven flow in a planar channel with the stress-integration method for the evaluation of hydrodynamic force acting on the cylinders. The simulation results show that the dumbbell also has the important feature of the Segré-Silberberg effect like a particle in a Poiseuille flow. The dumbbell trajectories, orientations, the cylinders vertical velocities and angular velocities all reach their equilibrium values separately independent of their initial positions. It is also found that the dumbbell equilibrium positions depend on the flow Reynolds number, blockage ratio and elastic coefficient. This study is expected to be helpful to understand the dynamics of polymer solutions, polymer synthesis and reaction, etc.