Many real world problems involve multiple criteria that should be considered separately and optimized simultaneously. A Multi-Objective Constraint Optimization Problem (MO-COP) is the extension of a mono-objective Constraint Optimization Problem (COP). In a MO-COP, it is required to provide the most preferred solution for a user among many optimal solutions. In this paper, we develop a novel Interactive Algorithm for MO-COP (MO-IA). The characteristics of this algorithm are as follows: (i) it can guarantee to find a Pareto solution, (ii) it narrows a region, in which Pareto front may exist, gradually, (iii) it is based on a pseudo-tree, which is a widely used graph structure in COP algorithms, and (iv) the complexity of this algorithm is determined by the induced width of problem instances. In the evaluations, we use an existing model for representing a utility function, and show empirically the effectiveness of our algorithm. Furthermore, we propose an extension of MO-IA, which can provide the more detailed information for Pareto front.