For a closed loop MIMO system to provide outstanding performance, the receiver needs to feedback accurate channel state information, which in turn requires a large codebook size. In this paper, we present a new codeword selection scheme based on a model-based channel estimator. Our scheme performs simultaneous channel estimation and codeword selection by exploiting the structures of the associated MIMO spatial channel and the codebook used. For a DFT-based codebook with arbitrary size, only a quantization operation is needed to select a proper codeword in a correlated fading environment. Using industry-approved standard channel models in simulating the system performance, we show that our low-complexity codeword selection scheme does outperform the scheme based on the conventional least-square estimator.