The construction industry is one of the major producers of municipal solid waste. Although there are many studies in municipal solid waste management, the research on the recovery of recyclable building material from construction sites remains limited. This paper addresses the optimal design issue of the construction and demolition (C&D) waste logistics network based on the features of the construction industry from the contractors’ perspective. The purpose of this paper is to provide an optimal C&D waste recycling network decision (RND) model considering the change of construction sites location over time. A multi-period and multi-objective mixed-integer linear programming model was developed to minimize the cost of C&D waste disposal for contractors, and to minimize the carbon emissions from C&D waste transportation. An application study was conducted to assess the performance of the RND model. Through some sensitivity analysis experiments based on an immune genetic algorithm, the influences of environmental policies and carbon tax policy on improving the recycling rate of C&D waste and reduce the carbon emission were explored. The findings of this research suggest that: (1) a RND model with the feature of the construction industry developed in this paper can effectively optimize the C&D waste logistics network; (2) government policies and laws are valid political instruments to improve the recycling rate of C&D waste; (3) the carbon-tax analyses demonstrate that a carbon tax policy can effectively reduce carbon emissions.