In this paper we formulate an integrable model on the simple cubic lattice. The N-valued spin variables of the model belong to edges of the lattice. The Boltzmann weights of the model obey the vertex-type tetrahedron equation. In the thermodynamic limit our model is equivalent to the Bazhanov-Baxter model. In the case when N = 2 we reproduce Korepanov's and Hietarinta's solutions of the tetrahedron equation as special cases.