In order to compute fluid flows in a transformable flow channel with deposition of fine particles using a level-set method, a re-initialization method for a time-varying level-set function (phi) describing the evolution of the geometrical shape of the sedimentation layer of fine particles was considered. It was shown that the choice of re-initialization method was very important to avoid non-physical deformation of phi. The re-initialization method was then applied to the problem with increments of phi (Delta phi), and net Delta phi was affected by the re-initialization method. To avoid this problem, we proposed a new re-initialization method that can maintain Delta phi. A multi-dimensional calculation of fluid flows with deposition of file particles could be implemented by using the proposed method.