This work proposes a supervised multi-objective optimization algorithm that assumes the existence of non-dominated solutions that serve as supervised data. In an expensive multi-objective optimization problem, it is required to obtain a solution set that approximates the Pareto front with an extremely small number of function evaluations. We often know some good solutions in advance when dealing with optimization problems. In this case, instead of generating solutions from scratch, generating solutions from known good solutions can be a shortcut for optimization. The proposed method estimates the Pareto front and Pareto set using the response surface methodology with existing non-dominated solutions as the supervised data. The proposed method selects a subset of objective vectors on the estimated Pareto front and obtains the subset as the solution set. Experimental results using DTLZ and WFG test suites show that the proposed method works well even with only ten non-dominated solutions and 150 function evaluations.