Abstract Private information retrieval (PIR) means a user retrieves a file while revealing no information on which file is being retrieved. In classic PIR, the user needs to wait for the responses of all the storage nodes. However, in general, there may be some nodes that are unresponsive, in which case it is formulated as v ‐robust PIR in the network coding (NC) structured distributed storage system (DSS), where v denotes the number of unresponsive nodes. We consider PIR with unresponsive nodes under the framework of NC structured DSS. In particular, the storage nodes adopt combination property with zigzag decodable (CP‐ZD) storage code since it has the advantage of extremely low decoding complexity, which is promised by zigzag decoding (ZD) within a binary field. We design a v ‐robust PIR scheme with its download communication cost slightly larger than existing studies, but its decoding complexity is significantly reduced when compared with existing studies.