A SrRuO3 thin film has been widely used as a metal electrode in electronic devices based on transition metal oxides, and hence it is important to understand its thermal transport properties to minimize a thermal degradation problem during the device operation. Using the time-domain thermoreflectance measurement technique, we investigate the cross-plane thermal conductivity of the SrRuO3 thin films with a thickness variation from 1 μm to 8 nm. We find that the thermal conductivity is reduced from about 6 W m-1 K-1 for the 1 μm thick film to about 1.2 W m-1 K-1 for the 8 nm thick film, and attribute this behavior to the boundary scattering of thermal carriers which originally have the mean free path of about 20 nm in a bulk state. Also, we observe a clear dip behavior of the thermal conductivity in the intermediate thickness around 30 nm which suggests an existence of a strong scattering source other than the film boundary. We explain this result by considering an additional interfacial scattering at the tetragonal-orthorhombic phase boundary which is formed during the strain relaxation with an increase of the film thickness.