The Smith-Purcell radiation of a charged particle moving in a periodic structure is analysed theoretically. The considered structure consists of two planar diffraction gratings with different periods which are formed by parallel conducting wires. The analytical expression for the spectral-angular distribution of radiation is obtained. It is shown that the angular distribution of radiation can be made narrower by using two gratings instead of one, and radiation intensity can be manipulated by parallel relative shift of gratings. The obtained results are of great importance for the research and development of high power radiation sources based on volume free-electron lasers.