This paper presents a multi-objective backbone guided search algorithm in order to optimize a bi-objective unconstrained binary quadratic programming problem. Our proposed algorithm consists of two main procedures which are hypervolume-based local search and backbone guided search. When the hypervolume-based local search procedure can not improve the Pareto approximation set any more, the backbone guided search procedure is applied for further improvements. Experimental results show that the proposed algorithm is very effective compared with the original multi-objective optimization algorithms.