The thermal conductivity of superlattice films is generally anisotropic and should be studied separately in the in-plane and cross-plane directions of the films. However, previous works have mostly focused on the cross-plane thermal conductivity because the electrons and phonons in the cross-plane direction of superlattice films may result in much stronger interface scattering than that in the in-plane direction. Nevertheless, it is highly desirable to perform systematic studies on the effect of interface formation in semiconducting superlattice films on both in-plane and cross-plane thermal conductivities. In this study, we determine both the in-plane and cross-plane thermal conductivities of Al2O3 (AO)/ZnO superlattice films grown by atomic layer deposition (ALD) on SiO2/Si substrates in the temperature range of 50-300 K by the four-point-probe 3-ω method. Our experimental results indicate that the formation of an atomic AO layer (0.82 nm) significantly contributes to the decrease of the cross-plane thermal conductivity of the AO/ZnO superlattice films compared with that of AO/ZnO thin films. The cross-plane thermal conductivity (0.26-0.63 W m-1 K-1 of the AO/ZnO superlattice films (with an AO layer of ∼0.82 nm thickness) is approximately ∼150%-370% less than the in-plane thermal conductivity (0.96-1.19 W m-1 K-1) of the corresponding film, implying significant anisotropy. This indicates that the suppression of the cross-plane thermal conductivity is mainly attributed to the superlattice, rather than the nanograin columnar structure in the films. In addition, we theoretically analyzed strong anisotropic behavior of the in-plane and cross-plane thermal conductivities of the AO/ZnO superlattice films in terms of temperature dependence.