This paper studies a problem of liner ship fleet planning with container transshipment under uncertain demand for container shipments. Generally, this problem can be solved with an optimization model to minimize or maximize the expected value of a key variable, such as cost or profit. However, such models do not consider the variance (namely, the risk), another issue of great concern to decision makers. Therefore, this paper aims to develop a robust optimization model in which both expected value and variance are considered simultaneously. By adjusting the penalty parameters of the robust optimization model, decision makers can determine an optimal plan for liner ship fleets (including decisions about fleet design and deployment) to maximize total profit under different container shipment demand scenarios while simultaneously controlling variance. The robustness and effectiveness of the developed model are demonstrated with numerical results.