In this paper, both backward and forward-type lens axicons illuminated by a Gaussian-Schell model (GSM) beam are studied. A numerical calculation is performed to investigate the axial intensity distribution of the focal segment. It is shown that when a backward-type lens axicon is illuminated with an appropriate beam radius and spatial coherence of the incident GSM beam, one can achieve a focal segment with uniform axial intensity. The rapid oscillation of the axial intensity can be reduced by the decreasing of spatial coherence. This method is very simple and efficient. A forward-type lens axicon illuminated by a GSM beam is also investigated.