A novel synthetic uniform circular array (SUCA) method for generating vortex electromagnetic (EM) wave carrying high orbital angular momentum (OAM) mode has the following steps. N antenna elements are placed radially to form a uniform circular array (UCA), where N is a positive integer. By rotating the array elements to various spatial locations, modifying their feeding phases, and superimposing the generated fields at various spatial locations, SUCA can beat the limit of space and configure more array elements to generate vortex electromagnetic (EM) waves carrying high mode OAMs. Meanwhile, due to the more synthetic array elements and smaller aperture than the traditional UCA, the purity of OAM mode is higher and it is more flexible to adjust the main lobe directions of these vortex waves carrying different OAM modes, and can generate vortex EM waves.