We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {α; β; k; t}, where k is the number of information symbols, each codeword of an (α; β; k; t)-group decodable code is a t-tuple of strings, called buckets, such that each bucket is a string of βsymbols that is a codeword of a [β; α] MDS code (which is encoded from αinformation symbols). Such codes have the following two properties: (P1) Locally Repairable: Each code symbol has locality (α; β-α+ 1). (P2) Group decodable: From each bucket we can decode αinformation symbols. We establish an upper bound of the minimum distance of (α; β; k; t)-group decodable code for any given set of {α; β; k; t}; We also prove that the bound is achievable when the coding field F has size |F| > n-1 \choose k-1.