Due to high carbon emissions in the logistics and distribution process, from a low carbon perspective, a Low Carbon Vehicle Routing Problem with Pickup and Delivery (LCVRPPD) considering fuzzy demand was formulated, and a 2-OPT based differential algorithm was proposed to solve the problem. In the algorithm, the natural number encoding method was adopted and three different fitness functions were given. Then, the 2-OPT algorithm was introduced to replace the original mutation mechanism of differential algorithm, and the binomial crossover operators and greedy selection operator were combined, so as to accelerate the convergence of the improved algorithm. In the case study, Taguchi method was used to determine reasonable values of parameters in the improved algorithm, and the SPSS (Statistical Product and Service Solutions) analysis revealed that the solution of the model with the minimum total cost as the objective function is the best compared to those of the other two different objective models of transportation cost minimization and carbon minimization respectively. For examples with different customer scales, compared with the basic differential algorithm, the improved algorithm has the total cost reduced by 1.8% to 3.0% and the carbon emission decreased by 0.7% to 3.5%; compared with genetic algorithm, the improved algorithm has the total cost reduced by 1.9% to 16.47% and the carbon emission decreased by 1.2% to 4.3%; compared with particle swarm optimization algorithm, the optimization effect is more obvious, the improved algorithm has the total cost reduced by 4.0% to 22.5% and the carbon emission decreased by 1.56% to 7.88%, which verify the effectiveness and advancement of the proposed algorithm. In summary, the proposed model and algorithm can provide a reference for the low carbon routing problem of pickup and delivery vehicles.