The performance of speed planning and energy management for connected and automated fuel cell hybrid vehicles (CAFCHVs) in the curve directly affects the curve passage, operating safety and energy economy. However, the uncertainty of complex traffic conditions (such as the dynamic state of the preceding and ego vehicle, road adhesion coefficient, and curve radius) and the lateral stability of CAFCHV lead to the difficulty of online speed planning and energy management. To address this problem, a co-optimization strategy is implemented in this study. First, according to the stability condition of CAFCHV in the curve, the critical safe speed is obtained by phase plane analysis. In addition, combing the timeliness, future information of driving conditions, and the current state of preceding and ego-vehicles, the gradient-based model prediction control (GRAMPC) leveraging the fast projection gradient method is adopted to calculate the safe and optimal speed sequence. Meanwhile, the energy management strategy (EMS) based on the power ratio adaptive equivalent consumption minimization strategy (PR-AECMS) is utilized for energy distribution. A multi-objective performance function is introduced to evaluate the total cost of hydrogen consumption and battery life extension. The simulation results reveal that the proposed strategy can obtain a safe and optimal speed sequence when CAFCHV operates on the curve road. And compared with the mode of tracking the speed of the preceding vehicle, the hydrogen consumption, SOC, battery degradation, and total cost are reduced by 1.4%, 1.9%, 9.9%, and 1.8% regulated by the planning mode, respectively.