Orbital angular momentum (OAM) modes can offer high density and high-capacity communication. The traditional phased array antenna can only produce a limited number of OAM beam modes l, usually less than half of the number of array elements (N): −N/2 < lmax < N/2. An OAM antenna array for generating high-order OAM modes is proposed in this letter. The proposed antenna array consists of a ring patch antenna that can generate vortex waves with OAM mode l = 1 or −1 and a phase-shifting feeding network. By adding different feed excitation signals to each element, the generated beam carries a higher-order mode: l = N or −N, breaking the previous limitations. Near-field measurements were conducted on antenna arrays composed of 3, 4, and 5 elements, revealing a high degree of correspondence between their phase distribution and radiation patterns with numerical simulation results. This alignment further substantiates the practical efficacy of this approach in significantly enhancing the generation of high-order OAM modes within antenna arrays. This advancement improves component utilization efficiency, reduces system complexity, and meets the high demands for spectral resources and channel capacity in future communication applications.