The stationary cosmological model without closed timelike curves of Gödel type is obtained for the ideal dust matter source within the framework of the teleparallel gravity. For a specific choice of the teleparallel gravity parameters, this solution reproduces the causality violating stationary Gödel solution in general relativity, in accordance with the teleparallel equivalent of general relativity. The relation between the axial-vector torsion and the cosmic vorticity is clarified. © 2004 Elsevier B.V. All rights reserved.