In distributed cloud storage sys-tems, inevitably there exist multiple node fail-ures at the same time. The existing methods of regenerating codes, including minimum storage regenerating (MSR) codes and mini-mum bandwidth regenerating (MBR) codes, are mainly to repair one single or several failed nodes, unable to meet the repair need of distributed cloud storage systems. In this paper, we present locally minimum storage re-generating (LMSR) codes to recover multiple failed nodes at the same time. Specifically, the nodes in distributed cloud storage systems are divided into multiple local groups, and in each local group (4, 2) or (5, 3) MSR codes are constructed. Moreover, the grouping method of storage nodes and the repairing process of failed nodes in local groups are studied. The-oretical analysis shows that LMSR codes can achieve the same storage overhead as MSR codes. Furthermore, we verify by means of simulation that, compared with MSR codes, LMSR codes can reduce the repair bandwidth and disk I/O overhead effectively.