In recent years, the need to build solid state drive (SSD)-based cloud storage systems has been increasing in order to process the big data generated by lots of Internet of Things devices and Internet users. Because these kinds of cloud systems require high performance and reliable storage, the use of flash-based Redundant Array of Independent Disks (RAID) will increase. But in flash-based RAID storage, parity data must be updated with every data write operation, which can more quickly overwhelm SSD's lifespan. To solve this problem, this letter proposes parity data deduplication for OpenStack cloud storage systems using an all flash array. Unlike the traditional data deduplication method, it only removes parity data, which will be stored in the parity disks of the all flash array. Experiments show that the proposed parity data deduplication method can efficiently reduce the number of parity data write operations, compared to the traditional data deduplication method.