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A novel concatenated multi-input multi-output (MIMO) communication system based on time varying linear transformation (TVLT) and Tanner codes is proposed in this paper. The girth 4 property of Tanner codes is discussed briefly. Combined with the outstanding distance property of Tanner codes, TVLT can provide full diversity and maximum coding gain at the same time without exhaustive search for the good space-time codes as usual. Corresponding joint iterative detector /decoder structure of receiver is given which greatly simplifies the demodulation /decoding process. Compared with present Turbo codes or conventional convolution codes concatenated MIMO system, the new concise system achieves higher coding gain and full diversity together, which is verified by simulation results.