This paper proposes a novel multi-objective distributed generation planning methodology in distribution network considering correlations among uncertainties, i.e., wind speed, light intensity and load demand. First, under the framework of chance constrained programming, a multi-objective distributed generation planning model with the objective functions of minimizing both the annual total cost and the risk is established. The constraints of the model contain not only the restrictions of distributed generation investment and various electrical limitations, but also the restrictions of correlations among uncertainties. Second, an efficient solving strategy is employed to solve the planning model, in which the correlation-handled probabilistic power flow is used to deal with the correlated uncertainties, and non-dominated sorting genetic algorithm H is applied to achieve the Pareto optimal set of the model. Last, case studies are carried out on two test distribution networks, and the results show that a balance between the economy and the security can be achieved by non-dominated sorting genetic algorithm II. The case studies also verify that the correlations among uncertainties can influence the multi-objective distributed generation planning results, and the stronger the correlation is, the bigger the influence will be.