We report on the growth of high-quality topological insulator BiSbTe3 films (thickness of 30nm) on sapphire (0001) substrates through the molecular beam epitaxy (MBE) technique and discuss the possibility to improve the film quality and surface flatness through annealing. Instead of using elemental Sb, the choice of Sb2Te3 as well as the use of solid sources of Bi and Te assures excellent stability during thermal evaporation enabling layer-by-layer epitaxial growth of high-quality films of BiSbTe3. The crystallinity and the terrace size of the BiSbTe3 films are found to be improved through increasing the deposition temperature and/or after annealing at 540K–620K for 1–4hours. The films grown at 485K, 500K, and 515K exhibit root-mean-square (RMS) roughness of 2.9nm, 2.3nm, and 2.3nm, respectively, whereas the RMS roughness is reduced to 0.6nm or less when the films are annealed at 580K for 2–4hours. Annealing the film at too high temperature, such as 620K, introduces a rougher surface due to the loss of material during annealing. A relatively low electron density of~2.2×1018cm-3 (at 2K) is achieved for the as-grown films deposited at 485K and 500K. Significantly enhanced electron density is found in the case of either increasing growth temperature or increasing annealing temperature. An exception is the film annealed at 620K, which became a p-type conductor. In addition, weak antilocalization effects are evident for the n-type films, but they nearly vanish for p-type conducting films. The significant influence of temperature on the crystallinity, the surface roughness, and the electronic transport in BiSbTe3 films will be instructive for further investigations of the transport behavior of surface states in BiSbTe3 films.