We have developed a new combinatorial synthesis system integrating a combinatorial shadow mask into a laser MBE (molecular beam epitaxy) chamber. This combinatorial Laser MBE system can be used for fabricating a number of crystalline films with different compositions on a substrate under programmed temperature and pressure conditions. The method was applied to alloying and band gap engineering of ZnO by positional substitution of ME into ZnO thin films. The superiority of the combinatorial methodology to conventional one-by-one synthesis is evident from the high linearity of the c-axis length and band gap dependence on Mg content.