An adaptive delay-tolerant distributed space-time coding (DSTC) scheme that exploits feedback is proposed for two-hop cooperative MIMO networks. Maximum likelihood (ML) receivers and adjustable code matrices are considered subject to a power constraint with a decode-and-forward (DF) cooperation strategy. In the proposed delay-tolerant DSTC scheme, an adjustable code matrix is employed to transform the space-time coded matrix at the relay nodes. Least-squares (LS) algorithms are developed with reduced computational complexity to adjust the parameters of the codes. Simulation results show that the proposed algorithms obtain significant performance gains and address the delay issue for cooperative MIMO systems as compared to existing delay-tolerant DSTC schemes.