In this paper, we focus on the facility location games with the property of dual preference. Dual preference property indicates that both two preferences of agents, staying close to and staying away from the facility (s), exist in the facility location game. We will explore two types of facility location games with this property, the dual character facility location game and the two-oppositefacility location game with limited distance which model the scenarios in real life. For both of them, we wish to design strategy-proof mechanisms or group strategyproof mechanisms with the objective of optimizing the social utility. For the dual character facility location game, we propose a strategy-proof optimal mechanism when misreporting is restricted to agents' preferences, and give a 1/3-approximation deterministic group strategy-proof mechanism when both location and preference are considered as private information. For the two-opposite-facility location game with limited distance, when the number of agents is even (denoted as 2k), we give a 1/k-approximation deterministic group strategy-proof mechanism, and when the number of agents is odd (denoted as 1/2k - 1), we propose a -approximation deterministic group strategy-proof mechanism. The approximation ratios for both mechanisms are proved to be the best a deterministic strategy-proof mechanism can achieve.