Vortex electromagnetic waves can carry orbital angular momentum (OAM) modes of different order number, which are mutually orthogonal. Communication technologies multiplexing different OAM topological charges have attracted extensive attention in improving spectrum utilization. In this regard, the efficient generation of OAM modes becomes a key issue. However, it is difficult to generate high‐order OAM modes by using a microstrip antenna with a simple structure, and the mode purity is usually not high. Methodologically, the OAM wave of a microstrip antenna is mostly achieved by synthesizing degenerate eigenmodes. In this paper, combined with eigenmode analysis, the construction of high‐order and high‐purity OAM mode microstrip antennas is carried out from the perspectives of radiating element, ground plane, and structural symmetry. For a regular hexagonal patch antenna of the 4th‐order OAM mode, the mode purity is improved from about 40% to over 80% by removing the inner conductor of the patch layer, using a circular ground plane, and adding lug patches on the outside. This method of improving mode purity through the analysis of mode significance and characteristic current distribution also has guiding significance for the design of other high‐order OAM mode patch antennas.