Assuming that there exists a dishonest coordinator, this paper studies the strategic manipulation problem in group decision making from a minimal cost perspective. First, a problem of manipulation individual preference with minimum cost in group decision making, and an approach of measuring minimum cost to obtain the coordinator’s desired alternative ranking are presented. Then, a strategic manipulation model on individual preference with minimum cost is developed to manipulate the ranking of alternatives. Furthermore, we establish the strategic manipulation model under weighted average (WA) and ordered weighted average (OWA), respectively. By setting different objective function value of the model, the performance of WA and OWA defending against strategic manipulation is compared. Finally, a numerical case is adopted to validate the effectiveness of proposed models, and two simulation experiments are designed to compare the impacts of changes in the number of decision-makers and the number of alternatives on the robustness of the WA and OWA aggregation functions against strategic manipulation of individual preferences.