Makespan and cost minimization are two important factors in project investment. This paper considers a multi-mode resource-constrained project scheduling problem with the objective of minimizing costs, subject to a deadline constraint. A number of studies have focused on minimizing makespan or resource availability cost with a specified deadline. This problem assumes a fixed cost for the availability of each renewable resource per period, and the project cost to be minimized is the sum of the variable cost associated with the execution mode of each activity. The presented memetic algorithm (MA) consists of three features: (1) a truncated branch and bound heuristic that serves as effective preprocessing in forming the initial population; (2) a strategy that maintains two populations, which respectively store deadline-feasible and infeasible solutions, enabling the MA to explore quality solutions in a broader resource-feasible space; (3) a repair-and-improvement local search scheme that refines each offspring and updates the two populations. The MA is tested via ProGen generated instances with problem sizes of 18, 20, and 30. The experimental results indicate that the MA performs exceptionally well in both effectiveness and efficiency using the optimal solutions or the current best solutions for the comparison standard.