Wave prediction in a coastal area, especially with complex geometry, requires a numerical simulation with a high-resolution grid to capture wave propagation accurately. The resolution of the grid from global wave forecasting systems is usually too coarse to capture wave propagation in the coastal area. This problem is usually resolved by performing dynamic downscaling that simulates the global wave condition into a smaller domain with a high-resolution grid, which requires a high computational cost. This paper proposes a deep learning-based downscaling method for predicting a significant wave height in the coastal area from global wave forecasting data. We obtain high-resolution wave data by performing a continuous wave simulation using the SWAN model via nested simulations. The dataset is then used as the training data for the deep learning model. Here, we use the Long Short-Term Memory (LSTM) and Bidirectional LSTM (BiLSTM) as the deep learning models. We choose two study areas, an open sea with a swell-dominated area and a rather close sea with a wind-wave-dominated area. We validate the results of the downscaling with a wave observation, which shows good results.