Direct administration of drugs with short half-lives can lead to low drug utilization rates. To solve this problem, a composite aerogel was prepared as the drug carrier with a high drug-loading ratio and excellent sustained release performance. In this study, cellulose was modified to carboxylated cellulose (CC) and then hydroxyapatite (HAP) and Cu nanoparticles were added as filler and coating respectively through blending and in situ synthesis methods. Importantly, The amount of 5-fluorouracil (5-Fu) drug loaded was 181 mg/g. The drug release time of the CC-HAP-Cu composite aerogel was 34 h (pH = 1) and 30 h (pH = 7.2), which indicated its excellent sustained release performance and pH responsiveness. By fitting and analyzing a kinetic model, the drug release of the CC-HAP-Cu aerogel was found to be primarily due to skeleton dissolution. In addition, the CC-HAP-Cu composite aerogel had good mechanical properties (6.70 MPa) and a low swelling ratio (1.7 g/g). Cytotoxicity was tested using the MTT method, and the relative cell viabilities were above 97%, which proved that the composite aerogel has excellent biocompatibility. Overall, the results indicated that CC-HAP-Cu aerogel is a promising drug carrier with potential application in medicine.