Program verification is one of the most important approaches to ensure the correctness of concurrent programs. However, due to the path explosion problem, concurrent program verification is usually time consuming, which significantly limits its scalability to industrial programs. Parallel processing is the most efficient technique to deal with those problems which require mass computing. Hence, designing parallel algorithms to improve the performance of concurrent program verification is highly desired. This paper focuses on parallelization of the abstraction refinement technique, one of the most efficient techniques for concurrent program verification. We have proposed a parallel refinement framework which employs multiple engines to refine the abstraction in parallel. Different from existing work which usually parallelizes the search process, our method achieves the effect of parallelization by refinement constraint and learnt clause sharing, such that the number of required iterations can be significantly reduced and the performance of constraint solving can be improved. We have implemented this framework on the scheduling constraint based abstraction refinement method, one of the best methods for concurrent program verification. Experimental results on SV-COMP 2018 show encouraging results of our method. For those complex cases requiring a large number of iterations, our method can obtain a linear reduce of the iteration number and significantly improve the verification performance.