We study the backward parabolic problem related to the convection-diffusion operator Au :equivalent to u(t) - (D(x)u(x))(x) + (c(x)u)(x) when the diffusion coefficient D(x) may be discontinuous. The forward collocation method (FC-method) is used for numerical solution of this backward transmission problem. According to the method, we approximate the unknown function phi(x) = (u(x, t(0)) by the piecewise linear continuous, Lagrange type of basis functions. Moreover, we solve the obtained ill-conditioned system of algebraic equations by using truncated singular value decomposition (TSVD). (C) 2009 Elsevier Ltd. All rights reserved.