A control volume finite-difference approach for the solution of axisymmetric laminar viscous flow through a converging-diverging pipe is presented. The pipe wall has a sinusoidal shape and constant enthalpy. The physical wavy domain is transformed into a rectangular computational domain to simplify the application of boundary conditions on the solid boundary. The governing equations in primitive variables are discretized on a control volume basis that ensures global as well as local conservation of mass, momentum, and energy. The pseudodiffusive terms that arise from the coordinate transformation are treated as source terms, and the resulting system of equations is solved by a semi-implicit procedure based on line relaxation. Results are obtained for both the developing and the fully developed flow for a Prandtl number of 0.72, ratio of pipe maximum diameter to pitch of 1.0, Reynolds number ranging from 100 to 500, and ratio of wall amplitude to pitch varying from 0.1 to 0.25.