Because Taiwan is located within the subtropical high and on the primary path of western Pacific typhoons, the interaction of these two factors easily causes extreme climate conditions, with strong wind carrying heavy rain and huge wind waves. To obtain precise wind-wave data for weather forecasting and thus minimize the threat posed by wind waves, this study proposes a two-step wind-wave prediction (TSWP) model to predict wind speed and wave height. The TSWP model is further divided into TSWP1, which uses data attributes at the current moment as input values and TSWP2, which uses observations from a lead time and predicts data attributes from input data. The classical one-step wave height prediction (OSWP) approach, which directly predicts wave height, was used as a benchmark to test TSWP. Deep recurrent neural networks (DRNNs) can be used to construct TSWP and OSWP approach-based models in wave height predictions. To compare with the accuracy achieved using DRNNs, linear regression, multilayer perceptron (MLP) networks, and deep neural networks (DNNs) were tested as benchmarks. The Guishandao Buoy Station located off the northeastern shore of Taiwan was used for a case study. The results were as follows: (1) compared with the shallower MLP network, the DNN and DRNN demonstrated a lower prediction error. (2) Compared with OSWP, TSWP1 and TSWP2 provided more accurate results. Therefore, the TSWP approach using a DRNN algorithm can effectively predict wind-wave heights.