Many real-world optimization problems can be modelled with several competing objectives. Most of the time, such optimization problems fall under the category of expensive problems. These are problems in which each fitness evaluation is time-consuming, for example, one fitness call could take hours or even days to compute. The time-consuming process of evaluating the function values or gradient of the objective functions may degrade the running speed of many optimization algorithms. The coordinate search (CS) approach is introduced as a single-objective gradient-free method for addressing large-scale, non-convex, and costly optimization problems. Due to the low computation and memory requirements of the CS algorithm, it can also be efficiently extended to address multi-objective optimization problems. The subject of this study is to develop a CS-based algorithm aimed at computationally expensive multi-objective optimization problems. In order to generate a set of non-dominated solutions, a population is created to apply the CS algorithm on each individual and finally reach an optimized interval. We demonstrate the efficacy of the proposed multi-objective CS method by comparing it with NSGA-II and MOEA/D as one of the well-known multi-objective algorithms on ZDT benchmark functions. Promising results are reported with the assumption of a limited number of fitness evaluations (NFF) which is desired during tackling complex and expensive optimization problems. Another major advantage of the proposed algorithm is that it provides regions of the Pareto front, that using sampling can generate as many Pareto front solutions as needed unlike other common optimization algorithms including NSGA-II.