The thermal conductivity of carbon nanotube (CNT) Y junctions and the thermal rectification behavior in the Y junctions have been investigated by means of classical non-equilibrium molecular dynamics simulation with quantum effects considered. The results indicate that the thermal conductivity of a CNT Y junction is about 12%–85% lower than a (10,10) pristine CNT. The thermal conductivity of the Y junction in the positive direction, when the heat flux is directed from the stem to branches, is always higher than that of the reverse direction, i.e. from branches to the stem. The decline of the thermal conductivity due to the existence of Y junctions decreases with increasing temperature. The thermal rectification coefficient of the Y junction first decreases and then increases with the increase of temperature.