This paper proposes an optimum design method for a two-dimensional microchannel heat sink under a laminar flow assumption that simultaneously provides maximal heat exchange and minimal pressure drop, based on a topology optimization method incorporating Pareto front exploration. First, the formulation of governing equations for the coupled thermal-fluid problem and a level set-based topology optimization method are briefly discussed. Next, an optimum design problem for a microchannel heat sink is formulated as a bi-objective optimization problem. An algorithm for Pareto front exploration is then constructed, based on a scheme that adaptively determines weighting coefficients by solving a linear programming problem. Finally, in the numerical example, the proposed method yields a Pareto front approximation and enables the analysis of the trade-off relationship between heat exchange and pressure drop, confirming the utility of the proposed method.