Refinery planning under uncertainty has gained tremendous attention, and this paper bridges deep learning and robust optimization to address this issue. First, we propose a large-scale mixed-integer linear programming model for refinery planning, where the fixed-yield models of the processing units are used. Prices of final products are considered uncertain parameters in the developed model to enhance the solution's applicability. Second, historical data of different products are collected to construct the uncertainty set characterizing all possible realizations of uncertainty. Third, a deep learning method is employed to capture the uncertainties of product prices, which has been proven to be powerful for high-dimensional price data. Based on the constructed uncertainty set, a data-driven robust optimization model is further developed. Finally, an iterative constraint generation algorithm is applied to solve the data-driven robust optimization problem. Case studies from an actual refinery are presented to showcase the effectiveness of the proposed method, which owes particularly to the representation capability of deep learning.