This study investigated the dissolved oxygen (DO) variation pattern in a Litopenaeus vannamei recirculating aquaculture system (RAS) and established an oxygen-utilization rate (UROxygen) model, pure oxygen addition (QOxygen) model, and control model that linked a microscreen drum filter (MDF) with a U-tube oxygenator. The main objective was to promote the application of the U-tube oxygenator and achieve the efficient, accurate, and automated management of DO in an RAS. To avoid wasting oxygen and ensure production safety, it was recommended to maintain the effluent of the aquaculture pond at 6.9 ± 0.4 mg/L. The modeled relationship between the RAS flow (QRAS), QOxygen, and UROxygen was UROxygen = 0.9626 × (−105.3406 + 0.9911QRAS + 10.6202QOxygen − 0.05964QRASQOxygen − 1.2628 × 10−3QRAS2 − 0.1821QOxygen2 + 6.8888 × 10−5QRAS2QOxygen + 6.3993 × 10−4QRASQOxygen2). The modeled relationship between QRAS, daily feeding rate (MFeeding), and QOxygen was QOxygen = 1.09 × (−12.8633 − 0.02793QRAS + 0.9369 MFeeding − 8.9286 × 10−4MFeedingQRAS + 5.6122 × 10−5QRAS2 − 2.3281 × 10−3MFeeding2). The modeled relationship between the MDF backwashing period (TMDF) and QOxygen was QOxygen = −11.57ln(TMDF) + 78.319. This study provided a theoretical basis and novel methods for the management of DO in an RAS, thus promoting the healthy and stable development of an L. vannamei RAS.