The thermal and electrical transport properties of single-crystalline LaBe13 have been investigated by specific-heat (C) and electrical-resistivity (rho) measurements. The specific-heat measurements in a wide temperature range revealed the presence of a hump anomaly near 40K in the C(T)= T curve, indicating that LaBe13 has a low-energy Einstein-like-phonon mode with a characteristic temperature of similar to 177 K. In addition, a superconducting transition was observed in the. measurements at the transition temperature of 0.53 K, which is higher than the value of 0.27K reported previously by Bonville et al. Furthermore, an unusual T-3 dependence was found in rho(T) below similar to 50 K, in contrast to the behavior expected from the electron-electron scattering or the electron-Debye phonon scattering.