The parity blocks of the Maximum-Distance-Separable （MDS） code are all global parity blocks. The length of the reconstruction chain increases with the expansion of the storage system， and the reconstruction performance gradually decreases. Aiming at the above problems， a new type of Non-Maximum-Distance-Separable （Non-MDS） code called local redundant hybrid code Code-LM（s，c） was proposed. Firstly， two types of local parity blocks called horizontal parity block in the strip-set and horizontal-diagonal parity block were added in any strip-sets to reduce the length of the reconstruction chain， and the parity layout of the local redundant hybrid code was designed. Then， four reconstruction formulations of the lost data blocks were designed according to the generation rules of the parity blocks and the common block existed in the reconstruction chains of different data blocks. Finally， double-disk failures were divided into three situations depending on the distances of the strip-sets where the failed disks located and the corresponding reconstruction methods were designed. Theoretical analysis and experimental results show that with the same storage scale， compared with RDP （Row-Diagonal Parity）， the reconstruction time of CodeM（s，c） for single-disk failure and double-disk failure can be reduced by 84% and 77% respectively； compared with V²-Code， the reconstruction time of Code-LM（s，c） for single-disk failure and double-disk failure can be reduced by 67% and 73% respectively. Therefore， local redundant hybrid code can support fast recovery from failed disks and improve reliability of storage system.