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High proportion of renewable energy and AC-DC hybrid structure are the challenges that the power system has faced. In order to cope with the high-dimensional uncertainties in the hybrid AC/DC system, this work developed a novel method of combining the uncertainty quantification and stochastic optimization to solve a hybrid AC-DC energy management problem. The problem is approximately reformulated by a conic quadratic optimization model, while a surrogate model of random variables and polynomial manipulation for a risk constraint are proposed to handle the tricky. Given a set of samples in the sparse random space generated by Smolyaks algorithm, thus the problem could be handled by using a high-performance solver. Simulation results verify that our proposed approach not only reduces the computational cost for energy management under uncertainties but also provides more accurate statistical information for risk assessment.