In order to improve the reliability of distributed storage systems and repair efficiency of failed nodes, locally repairable codes based on Pyramid codes are proposed in this paper. Specifically, adopting the minimum achievable encoding structure of Pyramid codes, the proposed locally repairable codes divide the nodes of distributed storage systems into multiple local repair groups, to achieve lower repair locality and rapid repair of failed nodes. The performance analysis shows that, the proposed locally repairable codes based on Pyramid codes can achieve rapid repair of multiple failed nodes in distributed storage systems, has lower repair locality. Moreover, compared with three copy replication strategies and simple regenerating codes, the proposed locally repairable codes based on Pyramid codes have advantages in the performances of storage overhead and repair bandwidth overhead.