Unconstrained binary quadratic programming problem (UBQP) consists in maximizing a quadratic 0-1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. Recently, a multi-objective UBQP (mUBQP) is defined and a set of mUBQP instances is proposed. This paper proposes a directional-biased tabu search algorithm (DTS) for mUBQP problem. In the beginning of the search, DTS optimizes the problem for each objective function to obtain extreme solutions. If extreme solution for one objective function cannot be further improved, the search gradually changes the direction and optimizes the problem along the new directions. The proposed algorithm is tested on 50 mUBQP benchmark instances, and experimental results show that DTS can obtain better solutions than the previous state-of-the-art algorithm for the mUBQP cases.