This paper addresses an airport gate assignment problem with multiple objectives. The objectives are to minimize the number of ungated flights and the total passenger walking distances or connection times as well as to maximize the total gate assignment preferences. The problem examined is an integer program with multiple objectives (one of them being quadratic) and quadratic constraints. Of course, such a problem is inherently difficult to solve. We tackle the problem by Pareto simulated annealing in order to get a representative approximation for the Pareto front. Results of computational experiments are presented. To the best of our knowledge, this is the first attempt to consider the airport gate assignment problem with multiple objectives.