This article deals with a short-term Liner Ship Fleet Planning (LSFP) problem with cargo shipment demand uncertainty for a single liner container shipping company. The cargo shipment demand uncertainty enables us to propose a chance constraint for each liner service route, which guarantees that the liner service route can satisfy the customers’ demand at least with a predetermined probability. Assuming that cargo shipment demand between any two ports on each liner service route is normally distributed, this article develops an integer linear programming model with chance constraints for the short-term LSFP problem. The proposed integer linear programming model can be efficiently solved by any optimization solver such as CPLEX. Finally, a numerical example is carried out to assess the model and analyze impact of the chance constraints and cargo shipment demand.