Recently, metasurfaces have been extensively studied, especially in connection with the construction of orbital angular momentum (OAM)-carrying beams. However, the dependence of OAM performance on the resolution of unit cells remains to be investigated. In this paper, 27 types of metalenses of varying phase resolutions (1-bit, 2-bit, and 3-bit) and with unit cells of varying width resolutions ( 1λ0, (1/2) λ0, and (1/3) λ0) were designed to analyze this dependence via simulation. A thorough analysis of the simulated results, including the radiation pattern, the near-field amplitude, the near-field phase, and the OAM mode purity, revealed that the OAM performance of a metalens improves with an increase in resolution. In addition, even metalenses of 1-bit phase resolution and 1λ0 width resolution were observed to exhibit OAM mode purities higher than 88%. We expect the conclusions of this study to be useful as guidelines during the future design of OAM metalenses or metasurfaces.