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Link recommendation, which recommends links to connect unlinked online social network users, is a fundamental social network analytics problem with ample business implications. Existing link recommendation methods tend to recommend similar friends to a user but overlook the user's diversity preference, although social psychology theories suggest the criticality of diversity preference to link recommendation performance. In recommender systems, a field related to link recommendation, a number of diversification methods have been proposed to improve the diversity of recommended items. Nevertheless, diversity preference is distinct from diversity studied by diversification methods. To address these research gaps, we define and operationalize the concept of diversity preference for link recommendation and propose a new link recommendation problem: the diversity preference-aware link recommendation problem. We then analyze key properties of the new link recommendation problem and develop a novel link recommendation method to solve the problem. Using two large-scale online social network data sets, we conduct extensive empirical evaluations to demonstrate the superior performance of our method over representative diversification methods adapted for link recommendation as well as state-of-the-art link recommendation methods.