Abstract: With increase of storage devices, the data placements based on toleration single or double failures can not meet the requirement of the reliability in the distributed storage systems. On the basis of the Row Diagonal Parity (RDP) code for double toleration failures, a new class of array codes for triple storage failures is presented which is called Extending Row Diagonal Parity (E-RDP) code. The E-RDP code has the Maximum Distance Separable (MDS) property, and it is optimal in redundancy rate and erasure correcting capability among triple erasure-correcting codes. The procedures of encoding and decoding are depicted by geometrical lines of different slope, then a fast decoding algorithm is given and it is more easily implemented by software and hardware. The theoretical analysis shows that the comprehensive properties of the E-RDP code such as encoding and decoding efficiency, small writes and balance performance, are better than other popular MDS codes, thus the E-RDP code is practically meaningful for storage systems.