In order to provide decision support for vehicle scheduling of logistics companies, this paper investigated the routing problem with time windows and dynamic demands considering a mixed fleet of electric and conventional vehicles, and proposed a two-stage integer programming model to minimize the total distribution cost. This paper designed an improved adaptive large-scale neighborhood search algorithm(IALNS), proposed the new deletion and repair operators and acceleration strategy in the dynamic stages. It conducted the extensive large-scale computational experiments with both static and dynamic demands to examine the performance of proposed IALNS. The results show that, compared to IALNS-ND, IALNS performs better in term of the minimum and average values in 75% of the static problems ( 9 out of 12 cases) . In 95% (57 out of 60 examples) of the dynamic cases, IALNS works better than IALNS-ND in terms of the cost and computation time . Moreover, compared to ALNS, LNS and VNS, IALNS performs best in term of the best minimum and average values of the total costs for all static cases. In 58% (35 out of 60 examples) of the dynamic case, the IALNS can achieve a better solution in 1.5 times or even 10 times less computation time than the rest algorithms. Also the larger the degree of dynamism of a experiment is, the better the obtained solution obtained by IALNS in a shorter time. Thus IALNS performs best in solving the time-sensitive dynamic demand vehicle routing problem. [ABSTRACT FROM AUTHOR]