Due to the salient DRAM-comparable performance, TB-scale capacity, and non-volatility, persistent memory (PM) provides new opportunities for large-scale in-memory computing with instant crash recovery. However, programming PM systems is error-prone due to the existence of crash-consistency bugs, which are challenging to diagnose especially with concurrent programming widely adopted in PM applications to exploit hardware parallelism. Existing bug detection tools for DRAM-based concurrency issues cannot detect PM crash-consistency bugs because they are oblivious to PM operations and PM consistency. On the other hand, existing PM-specific debugging tools only focus on sequential PM programs and cannot effectively detect crash-consistency issues hidden in concurrent executions.In order to effectively detect crash-consistency bugs that only manifest in concurrent executions, we propose PMRace, the first PM-specific concurrency bug detection tool. We identify and define two new types of concurrent crash-consistency bugs: PM Interthread Inconsistency and PM Synchronization Inconsistency. In particular, PMRace adopts PM-aware and coverage-guided fuzz testing to explore PM program executions. For PM Inter-thread Inconsistency, which denotes the data inconsistency hidden in thread interleavings, PMRace performs PM-aware interleaving exploration and thread scheduling to drive the execution towards executions that reveal such inconsistencies. For PM Synchronization Inconsistency between persisted synchronization variables and program data, PM-Race identifies the inconsistency during interleaving exploration. The post-failure validation reduces the false positives that come from custom crash recovery mechanisms. PMRace has found 14 bugs (10 new bugs) in real-world concurrent PM systems including PM-version memcached.