A novel plate-like covalent organic framework (COF) adsorbent (AO-MA-ATA) was synthesized via a series of thermochemical methods using amidoxime-functionalized 2-aminoterephthalic acid (H2ATA)-melamine (MA) and applied for the removal of radioactive uranium U(VI) under neutral aqueous conditions. The prepared materials were characterized using spectroscopic, X-ray, and microscopic imaging techniques, which confirmed the plate-like structure of the AO-MA-ATA COFs. Kinetic analysis indicated that U(VI) adsorption onto AO-MA-ATA followed a second-order model. The isothermal adsorption of U(VI) could be described by the Langmuir isotherm model, with a maximum adsorption capacity of 1111.1 mg g−1 at 318 K and pH 7. Evaluation of the thermodynamic parameters showed that U(VI) adsorption by AO-MA-ATA was a spontaneous and exothermic process. The adsorption mechanism mainly involved chelation, rather than covalent bonding. Overall, the results presented herein indicate that AO-MA-ATA COFs can effectively remove U(VI) from aqueous solutions and are therefore promising candidates for treating uranium-containing wastewater.