This paper investigates the bunker procurement planning (BPP) problem arising for a container liner shipping company that plans to purchase bunker from both bunker futures contracts and the spot market to hedge the risk in fluctuation of and increases in bunker prices. A multistage bunker procurement decision process for the BPP problem is developed to determine the monthly bunker procurement. The process allows the shipping company to sign bunker futures contracts in the first stage and to rebalance them in the subsequent stages. By assuming the stochasticity of bunker spot price, the BPP problem is formulated as a mean-variance minimization stochastic programming model. An approximation solution method for solving this model is designed by integrating random variable sampling technique, scenario tree generation, and quadratic programming approximation. Finally, numerical experiments demonstrate that bunker procurement risk can be effectively hedged with the proposed method. This study provides a useful decision tool for container liner shipping companies to use when planning bunker procurement.