Aiming at the location problem of low carbon logistics distribution center, a location model that takes the lowest total cost including carbon emission costs as the goal and the uncertainty requirements as the random constraint is proposed, with stochastic programming theory, the model is validated to be effective by the use of actual examples. It is proved that the model can provide a certain reference value for the location investment and income of the enterprise under the fluctuation of actual market demand. In addition, the sensitivity analysis of confidence level and standard deviation of the uncertainty demand is carried out, which shows that the uncertainty of carbon emission and demand have significant impacts on the distribution center location results; the total cost of location is closely related to the degree of uncertainty of demand, and the cost of carbon emissions will also fluctuate greatly with changes in demand.