[en] Transport of the chain of Brownian particles driven by a constant force is investigated in steady laminar flow. Within tailored parameter regimes, this system exhibits absolute negative mobility (ANM), which means that the chain travels in a direction opposite to the external force. When the constant force is applied to all particles, the phenomenon of ANM is observed for large spring constant. When the force is applied to the first particle of the chain, the emergence of ANM can occur for both small and large spring constant. In addition, we can obtain multiple current reversals by suitably changing the spring constant. (paper: classical statistical mechanics, equilibrium and non-equilibrium)