Corn (Zea mays) grown in the southern Piedmont requires 200 to 280 kg nitrogen (N) ha−1 annually and requires up to 0.87 cm of water per day, making groundwater systems susceptible to nitrate (NO3−) leaching. A perennial white clover (Trifolium repens L.) living mulch (LM) system may reduce NO3-N leaching by using legume N to replace mineral N, though little information is available on such a system in the southern Piedmont. Therefore, a HYDRUS-1D model was used to simulate water and NO3-N flux in three cover crop systems. Cereal rye (Secale cereal L.) (CR), crimson clover (Trifolium incarnatum L.) (CC), and a white clover LM were fertilized with 280, 168, and 56 kg N ha−1. The HYDRUS-1D model was calibrated and validated with observed water contents and NO3-N data that were collected over two years. Water and NO3-N flux models were created for each treatment and evaluated using coefficient of determination, percentage bias, and index of agreement, and showed good agreement to observed data. Nitrate leaching below 1 m in 2015/2016 was 23.5, 12.7, and 21.4 kg ha−1 for the CC, LM, and CR treatments, respectively, but was less than 1 kg ha−1 for all treatments in 2016/2017 due to prolonged drought. Differences in leached NO3-N among treatments were attributed to variation in mineral N application rate and NO3-N uptake by cover crops. Overall, results suggest that the use of a perennial LM system may reduce NO3-N leaching when compared to annual CC and CR cover crop systems.