In this report, alpha-In2Se3 single-crystal nanobelts and nanowires were grown in the thermal chemical vapor deposition furnace. The growth direction of the nanobelts was identified by standard microscopy techniques and was along the in-plane direction, while that of the nanowire was along the c-axis. The temperature-dependent thermal conductivity of the nanostructures was measured by a suspended-pattern technique, and it was found to fall into two ranges of values between 300 and 400 K owing to the difference in growth orientation. The experimental evidence presented herein is the anisotropy of phonon transport of the layered alpha-In2Se3, and the effect of bonding strength on the thermal conductivity at the nanoscale. This study would be helpful to the physical understanding and future design of In2Se3-based thermoelectric materials.