High-power orbital angular momentum (OAM) beams have distinct advantages in improving capacity and data receiving for free-space optical communication systems at long distances. Utilizing the coherent combination of a beam array technique and helical phase approximation by a piston phase array, we have proposed a generating system for a novel high-power beam carrying OAM, which could overcome the power limitations of a common vortex phase modulator and a single beam. The characteristics of this generating method and the orthogonality of the generated OAM beams with different eigenstates have been theoretically analyzed and verified. Also a high-power OAM beam produced by coherent beam combination (CBC) of a six-element hexagonal fiber amplifier array has been experimentally implemented. Results show that the CBC technique utilized to control the piston phase differences among the array beams has a high efficiency of 96.3%. On the premise of CBC, we have obtained novel vortex beams carrying OAM of $\pm 1$ by applying an additional piston phase array modulation on the corresponding beam array. The experimental results agree approximately with the theoretical analysis. This work could be beneficial to areas that need high-power OAM beams, such as ultra-long distance free-space optical communications, biomedical treatments, and powerful trapping and manipulation under deep potential wells.