In this paper, we propose a model-free unsupervised learning approach to forecast real-time locational marginal prices (RTLMPs) in wholesale electricity markets. By organizing system-wide hourly RTLMP data into a 3-dimensional (3D) tensor consisting of a series of time-indexed matrices, we formulate the RTLMP forecasting problem as a problem of generating the next matrix with forecasted RTLMPs given the historical RTLMP tensor, and propose a generative adversarial network (GAN) model to forecast RTLMPs. The proposed formulation preserves the spatio-temporal correlations among system-wide RTLMPs in the format of historical RTLMP tensor. The proposed GAN model learns the spatio-temporal correlations using the historical RTLMP tensors and generate RTLMPs that are statistically similar and temporally coherent to the historical RTLMP tensor. The proposed approach forecasts system-wide RTLMPs using only publicly available historical price data, without involving confidential information of system model, such as system parameters, topology, or operating conditions. The effectiveness of the proposed approach is verified through case studies using historical RTLMP data in Southwest Power Pool (SPP).