To optimize wind farm layout and improve wind energy conversion, it is significant to accurately and efficiently model wind turbine wake. In this study, a novel dimensionality reduction method, i.e., delayed proper orthogonal decomposition (d-POD) is proposed and combined with long short-term memory (LSTM) network to predict the unsteady wind turbine wake velocity. Compared with standard POD, d-POD can extract coherence modes and mode coefficients that could highlight the main feature and smooth the noise, so that it achieves higher accuracy. Meanwhile, the deep network LSTM is employed to predict the temporal evolution of mode coefficients. Accordingly, the velocity distribution is reconstructed by the predicted mode coefficients and coherence mode. The proposed wake prediction surrogate model is validated by high-fidelity large eddy simulation data. Results show that d-POD-LSTM model can fast and precisely predict the unsteady wind turbine wake dynamics similarly as high-fidelity wake of LES for both near wake and far wake. More importantly, compared with conventional POD-LSTM model (i.e., delayed number d = 1), the performance of d-POD-LSTM model is superior. As delayed number increases from 1 to 16, the prediction error of d-POD coefficient reduces by 80%, and thus the wake prediction error decreases accordingly.