Construction site layout planning is a fundamental task for any project undertaking. In practice, most of construction site layout planning problems are dynamic, multi-objective and uncertain in nature. To enhance the general practice of dynamic construction site layout planning, this paper proposes a fuzzy random multi-objective decision making model. In this model, two objectives are considered: (1) minimizing the total cost of site layout: and (2) maximizing the distance between the 'high-risk' facilities and the 'high-protection' facilities to reduce the possibility of safety or environmental accidents. After stating the problem and presenting the mathematical formulation, this paper deals with fuzzy random variables to propose an equivalent crisp model. According to the characteristics of the proposed model, a multi-objective particle swarm optimization algorithm (MOPSO) with permutation-based representation is proposed to solve the problem. The approach is applied to the Longtan hydropower construction project to illustrate the effectiveness of the proposed model and algorithm.