We consider a maritime inventory routing problem in the liquefied natural gas (LNG) business. Here, an actor is responsible for the routing of the fleet of special purpose ships, and the inventories both at the liquefaction plants and at the regasification terminals. The LNG inventory routing problem includes some complicating aspects compared to many other maritime inventory routing problems such as 1) a constant rate of the cargo evaporates each day and is used as fuel during transportation, 2) variable production and consumption of LNG, and 3) a variable number of tanks unloaded at the regasification terminals. The problem is solved by a branch-and-price-and-cut method. In the column generation approach, the master problem handles the inventory management and the port capacity constraints, while the subproblems generate the ship route columns. Different accelerating strategies are implemented. The proposed method is tested on instances inspired from real-world problems faced by a major energy company.