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An adaptive distributed space-time coding (DSTC) scheme and algorithms are proposed for two-hop cooperative MIMO networks. Linear minimum mean square error (MMSE) receivers and an amplify-and-forward (AF) cooperation strategy are considered. In the proposed DSTC scheme, an adjustable matrix obtained by a feedback channel is employed to transform the space-time coded matrix at the relay node. Linear MMSE expressions are devised to compute the parameters of the adaptive matrix and the linear receive filter. A stochastic gradient algorithm is also developed to compute the parameters of the adaptive matrix with reduced computational complexity. We also derive the upper bound of the error probability of a cooperative MIMO system employing the randomized space-time coding scheme first. The simulation results show that the proposed algorithms obtain significant performance gains as compared to existing DSTC schemes.