Summary: In the present paper a fixed charge bi-criterion quadratic transportation problem with restriction on the total flow is studied. An algorithm to find the efficient cost-time trade off pairs in a fixed charge bi-criterion quadratic transportation problem is presented. A related fixed charge bi-criterion quadratic transportation problem is formulated and the efficient cost-time trades off pairs to the given problem are shown to be derivable from this related problem. The algorithm is illustrated with the help of a numerical example.