A new MDO algorithm named as Subspace Decomposition and Discarding Optimization (SDDO) is advanced here. The optimization is based on the approximation model, of which the main idea is based on the subspace decomposition and discarding. Firstly, the approximation model of a MDO problem was carried on its design space. If the precision of approximation model reaches a satisfying precision, this optimization procedure will be terminated. Otherwise, the design space will be decomposed into two or more subspaces. Then, the optimization will be carried on the approximation of these subspaces. If the subspace has no promise to get better optimization result than the optimum reached by other subspaces, the subspace will be discarded. If the subspace approximation precision has reached a satisfying precision, this subspace will not be decomposed into smaller subspace. If the subspace has not reached a satisfying precision and has promise to get better optima, this subspace will be decomposed into smaller subspaces. The calculation time of this process is related to the numbers of design variables and design space. Function optimization examples show that this optimization algorithm has good performance on calculation time and global optima.