Under the background of renewable-dominated electric power system construction, the penetration rate of low-carbon and renewable distributed generation (DG) in distribution network is increasing, which has changed the form and operation mode of the distribution network. To deal with the output fluctuation of high penetration DG in the distribution network operations, it is necessary to evaluate the acceptance capacity of DG. The correct evaluation can realize the secure, economic and low-carbon configuration of DG. In this paper, an evaluation method of acceptance capacity of DG in the distribution network considering the carbon emission is proposed. Firstly, a multi-objective evaluation model of acceptance capacity of DG is constructed with the objectives of minimizing carbon emission in the full life cycle, minimizing node voltage deviation and maximizing line capacity margin. Secondly, the improved non-dominated sorting genetic algorithm II (NSGA-II) is employed to solve the model to determine the Pareto optimal solutions of DG configuration. Then, the comprehensive index of acceptance capacity evaluation is obtained based on entropy weight method to decide the optimal compromise solution. Finally, an actual 55-bus distribution network in China is used to verify the effectiveness of the proposed method. The simulation results show that the proposed evaluation method can comprehensively obtain the optimal compromise solution considering the reliability, economy and carbon emission benefits of distribution network operation, which guides the DG configuration in the distribution network.