Adsorption and photocatalytic degradation are effective strategies to purify the wastewater caused by organic dyes. In this study, graphitic carbon nitride (g-C3N4) powders are prepared from melamine with a thermal decomposition method, which are applied to synthesize the direct Z-scheme g-C3N4-ZnO@graphene aerogel (g-C3N4-ZnO@GA) heterojunctions with a hydrothermal self-assembly combined with freeze-drying. As adsorbents and photocatalysts, the heterojunctions exhibit superior adsorption capacity and catalytic activity for the elimination of organic pollutants irradiated by UV and visible light. Among all the materials, g-C3N4-ZnO@GA(30%) displays the best purification efficiencies of rhodamine B (RhB) under both UV and visible light illumination, reaching 81.0% and 82.7%, respectively, because of its hierarchical porous structure and the synergistic effect among the components. More importantly, g-C3N4-ZnO@GA(30%) possesses good reusability, which can keep 87.1% of the initial activity after four cycles. What's more, the heterojunctions also demonstrate high removal efficiency for other organic dyes, such as methyl orange (MO), demonstrating their promising application in environmental remediation. Finally, based on the experimental investigations, a reasonable photocatalytic mechanism is proposed and analyzed. The present work provides a promising way to construct the direct Z-scheme porous heterojunctions for elimination of environmental pollutants.