The importance of dynamic multi-objective optimization problems (DMOPs) is on the rise, in complex systems. DMOPs have several objective functions and constraints that vary over time to be considered simultaneously. As a result, the Pareto optimal solutions (POS) and Pareto front (PF) will also vary with time. The desired algorithm should not only locate the optima but also track the moving optima efficiently. In this paper, we propose a new Cultural Algorithm (CA) based on decomposition (CA/D). The primary objective of the CA/D algorithm is to decompose DMOP into several scalar optimization subproblems and solve simultaneously. The subproblems are optimized utilizing the information shared only by its neighboring problems. The proposed CA/D is evaluated using CEC 2015 optimization benchmark functions. The results show that CA/D outperforms CA, Multi-population CA (MPCA), and MPCA incorporating game strategies (MPCA-GS), particularly in hybrid and composite benchmark problems.