Thin films of Ca1-xSrxCuO2 have been prepared on SrTiO3 (100) substrates by co-deposition of all elements and successive stacking of atomic layers. When all the elements are deposited simultaneously, Ca1-xSrxCuO2 films can be formed only within the narrow range of Sr concentration near x=0.2. On the other hand, by stacking atomic layers of Ca(Sr)Ox and CuOx, the appropriate range becomes much wider and the formation of an infinite layer structure becomes possible, even in Ca free composition, SrCuO2. For the SrCuO2 thin film, a diamagnetic transition and decrease of resistance have been observed at 65 K.