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In this paper, we propose a quantized predictive precoding scheme for spatial multiplexing multiple- input multiple-output (MIMO) systems with delayed feedback. A geodesic transmit subspace prediction algorithm is designed to predict the transmit subspace for the forthcoming transmission at the receiver. An infrequently updated codebook for transmit subspace quantization is developed to improve the quantization resolution. Numerical results show that in various time-varying channels with unit step feedback delay the performance of the proposed approach is better than previously proposed memoryless Grassmannian subspace packing scheme, the 1-bit geodesic feedback algorithm, and the Gaussian vector quantization algorithm, under the same or even lower feedback rate.