In civil engineering management, under the background of carbon neutrality, there is a strong correlation and mutual constraints between cost, duration, and quality, and all civil engineering management must grasp cost control and multi-objective equilibrium. In this paper, the objective functions of duration, cost, and quality are constructed, the multi-objective equilibrium model of duration-cost-quality of civil engineering management is designed, and an improved non-dominant ranking genetic algorithm with elite strategy is constructed for solving the mathematical problem of multi-objective optimization. Finally, the model is used to analyze the case of a three-story mixed-structure office building, and it is found that the total cost of the model is 1089048 yuan, and the calculation is stopped when the programming cycle is 10096 times. Among them, scheme 1 has 146 working hours, a cost of 1.765 million yuan, and a quality of 0.95. Scheme 2 has 161 working hours, a cost of 1.693 million yuan, and a quality of 0.94. Scheme 3 has 176 working hours, a cost of 1.917 million yuan, and a quality of 0.99, and the specific plan can be selected according to the preference of the decision-maker. The model and algorithm’s effectiveness and matching are verified by analyzing actual data. This study enriches the theory of multi-objective optimization problems in engineering projects and provides a practical approach to managing project objectives.