We investigate theoretically the field-free orientation of CO molecules induced by a single-cycle THz laser pulse train. It is shown that the molecular orientation can be obviously enhanced by applying the pulse train. The laser intensity and pulse number have some effects on the molecular orientation. The high degree of field-free molecular orientation $|$$〈$cos$θ$$〉$$|$_max=0.9246 is obtained at temperature $T$=0 K. The variations of the maximum orientation degree with the experimentally available pulse number and peak intensity are given. Temperature $T$ has a considerable influence on the field-free molecular orientation. The maximal field-free molecular orientation at $T$=0, 10, 20 and 30 K for $N$=14 and $E_0$=1.8 MV/cm are $|$$〈$cos$θ$$〉$$|$_max=0.9188, 0.7338, 0.6055 and 0.5154 in order, and the corresponding effective duration times of molecular orientation are $∆t$=0.759, 0.432, 0.297 and 0.117 ps.