We construct a topological one-dimensional ladder model following the steps which lead to the Kane-Mele model in two dimensions. Starting with a Creutz ladder we modify it so that the gap closure points can occur at either  or . We then couple two such models, one for each spin channel, in such a way that time-reversal invariance is restored. We also add a Rashba spin-orbit coupling term. The model falls in the CII symmetry class. We derive the relevant  topological index, calculate the phase diagram and demonstrate the existence of edge states. We also give the thermodynamic derivation (Středa-Widom) of the quantum spin Hall conductance. Approximate implementation of this result indicates that this quantity is sensitive to the topological behavior of the model.