The present paper describes a numerical solution of shape optimization problems for non-stationary Navier-Stokes problems. As a concrete example, we consider the problem of finding the shape of an obstacle in a flow field in order to minimize the energy loss integral for an assigned time interval. The primary goal of the present paper is to demonstrate the evaluation of the shape derivative of the energy loss. The traction method is used for the reshaping algorithm. Numerical results show that the shapes of the circle obstacle converge to wedge shapes for the cases of Reynolds numbers of 100 and 250.