While the implementation of renewable energy systems and model predictive control (MPC) could reduce non-renewable energy consumption, one challenge to building climate control using MPC is the weather forecast uncertainty. In this work, we propose a data-driven robust model predictive control (DDRMPC) framework to address building climate control with renewable hybrid energy systems under weather forecast uncertainty. The control and energy system configurations include heating, ventilation, air conditioning, geothermal heat pump, photovoltaic panel, and electricity storage battery. Historical weather forecast and measurement data are gathered from the weather station to identify the forecast errors and for the use of uncertainty set construction. The data-driven uncertainty sets are constructed with multiple machine learning techniques, including principal component analysis (PCA) with kernel density estimation (KDE), K-means clustering coupled with PCA and KDE, and Dirichlet process mixture model (DPMM). Lastly, a data-driven robust optimization problem is developed to obtain the optimal control inputs for a building with renewable energy systems. A case study on controlling a building with renewable energy systems located on the Cornell University campus is used to demonstrate the advantages of the proposed DDRMPC framework.