Metocean conditions during hurricanes are defined by multiple parameters (e.g., significant wave height and surge height) that vary in time with significant auto- and cross-correlation. In many cases, the nature of the variation of these characteristics in time is important to design and assess the risk to offshore structures, but a persistent problem is that measurements are sparse and time history simulations using metocean models are computationally onerous. Surrogate modeling is an appealing approach to ease the computational burden of metocean modeling, however, modeling the time-dependency of metocean conditions using surrogate models is challenging because the conditions at one time instant are dependent on not only the conditions at that instant but also on the conditions at previous time instances. In this paper, time-dependent surrogate modeling of significant wave height, peak wave period, peak wave direction, and storm surge is explored using a database of metocean conditions at an offshore site. Three types of surrogate models, including Kriging, Multilayer Perceptron (MLP), and Recurrent Neural Network with Gated Recurrent Unit (RNN-GRU), are evaluated, with two different time-dependent structures considered for the Kriging model and two training set sizes for the MLP model, resulting in a total of five models evaluated in this paper. The performance of the models is compared in terms of accuracy and sensitivity towards hyperparameters, and the MLP and RNN-GRU models are demonstrated to have extraordinary prediction performance in this context.