Concept lattice, the core data structure in formal concept analysis, has been used widely in machine learning, data mining and knowledge discovery, information retrieval, etc. The main difficulty with concept lattice-based system comes from the lattice construction itself. This paper proposes a new algorithm called SSPCG (search space partition based concepts generation) based on the closures search space partition. The algorithm divides the closures search space into several subspaces in accordance with the criterions prescribed ahead, and introduces an efficient scheme to recognize the valid ones, which bounds searching just in these valid subspaces. An intermediate structure is employed to judge the validity of a subspace and compute closures more efficiently. Since the partition of the search space is recursive and the searching in subspaces is independent, a parallel version can be directly reached. The algorithm is experimental evaluated and compared with the famous NextClosure algorithm proposed by Ganter for random generated data, as well as for real application data. The results show that the algorithm performs much better than the later.