In this paper, we address the challenges of frequent backup and recovery operations associated with an unstable energy supply in energy-harvesting nonvolatile processors (NVPs). To address this problem, this paper adopts a retention state, which can allow the system to retain data in a volatile cache to wait for power recovery instead of immediately backing up the data. In addition, in an energy-harvesting NVP, important issues include how to back up and recover data, how to perform cache replacement, and how to transmit data to different parts of the cache in such a way that the performance and energy consumption can be improved and a successful backup can be guaranteed. Therefore, we propose a performance-oriented cache management scheme based on a retention state to generate near-optimal data migration, replacement and backup solutions for applications in polynomial time. This scheme uses two energy thresholds to pre-back up and back up data to reduce the backup and recovery operations according to the retention state. We evaluate the performance and energy consumption of our proposed algorithms in comparison with those of the dual-threshold SLC STT-RAM scheme and morphable cache scheme. The evaluation shows that the proposed scheme can achieve 18.58% and 4.54% lower average energy consumption than the SLC STT-RAM and morphable cache schemes, respectively, with comparable performance. The experimental results also show that compared with the SLC STT-RAM and morphable cache schemes, the proposed algorithm can achieve 17.90% and 8.85% performance improvement, respectively, on average.