The thermal transport properties of hexagonal boron nitride nanoribbons (BNNRs) are investigated. By calculating the phonon spectrum and thermal conductance, it is found that the BNNRs possess excellent thermal transport properties. The thermal conductance of BNNRs can be comparable to that of graphene nanoribbons (GNRs) and even exceed the latter below room temperature. A fitting formula is obtained to describe the features of thermal conductance in BNNRs, which reveals a critical role of the T(1.5) dependence in determining the thermal transport. In addition, an obviously anisotropic thermal transport phenomenon is observed in the nanoribbons. The thermal conductivity of zigzag-edged BNNRs is shown to be about 20% larger than that of armchair-edged nanoribbons at room temperature. The findings indicate that the BNNRs can be applied as important components of excellent thermal devices.