Ideal anion-exchange membranes (AEMs) for anion-exchange membrane fuel cells (AEMFCs) must possess high OH − conductivity, excellent alkaline resistance, good thermal stability, and improved dimensional stability. In this study, four types of poly(crown ether) (PCE) cross-linked AEMs containing different aromatic or alicyclic dicarboxylic acids were prepared for AEMFCs. The hydrophilic/hydrophobic polarity discrimination of AEMs can be adjusted by the introduction of various diacids into the polymer backbones. As a result, an obvious microphase-separated structure will form in AEMs, which may aid the movement of hydroxide ions. The as-prepared QAPCE-1.4P membranes with 1,4-phenylenediacetic acid as the dicarboxylic acid exhibit a distinct micromorphology separation, as confirmed by morphology characterization using small-angle X-ray scattering, atomic force microscopy, as well as transmission electron microscopy. The highest hydroxide ion conductivity of QAPCE-1.4P at 80 °C in ultrapure water is 133.25 mS cm −1 . Meanwhile, QAPCE-1.4P shows an improved dimensional stability at 80 °C with a swelling ratio of 10.83%. In addition, QAPCE-1.4P shows good chemical stability (96.1% ionic conductivity retention) even after being put in harsh alkali conditions at 80 °C for 40 days. Furthermore, the maximum power density of a single cell using QAPCE-1.4P as the polymer electrolyte membranes can reach 689 mW cm −2 in hydrogen/oxygen (80 °C).