Flow and heat transfer characteristics of fully developed laminar forced convection in two kinds of periodically converging-diverging passages are studied numerically in the body-fitted coordinates. In the computation, the water is severed as the working fluid and the wall temperatures are kept constant. The periodical boundary conditions are implemented by extending the computational domain and mutually replacing the variables in the corresponding locations. The entry height and the cross area of the both passages are identical. The heat transfer characteristics of the both passages are compared under the conditions of the identical mass flux, identical pressure drop and identical pumping power. It is found that the wave-like passage is superior to the linear passage under the condition of the identical mass flux and pumping power and inferior to the linear passage under the condition of the identical pressure drop when the Reynolds is less than 1 000.