Due to the orthogonality, multiple orbital angular momentums (OAMs) have great potential for increasing communication capacity and improving imaging resolution. In this work, a general N‐arm Archimedean spiral antenna (ASA) synthesis method is proposed for generating broadband vortex waves carrying multiple OAMs. In the proposed method, the theoretical formulas of the whole OAM modes based on the improved current band theory for N‐arm ASA and the maximum common bandwidth of each N‐adjacent OAM mode are presented. The performance of the proposed method is verified by simulated results of three‐arm ASA, as well as simulated results and measured results of four‐arm ASA. The measured results show that the four‐arm ASA generates vortex waves carrying OAM modes of l = 0, 1, 2, 3 in 0.6–3, 1.4–3.8, 2.3–4.1 and 2.6–4.5 GHz. And the maximum common bandwidth of the four generated OAM modes is 2.6–3 GHz, which satisfies the design requirement of OAM's practical application.