Considering a reverse supply chain composed of a remanufacturer, on-line and off-line competitive recyclers and consumers, this paper studies the differential game problem of reverse supply chain under the background of competition. The stochastic evolution process of advanced remanufacturing technology is described by using ito process. Based on the profit structure of members, the stochastic differential game model of reverse supply chain is constructed. By using Bellman's continuous dynamic programming theory, the members' feedback strategies under dynamic and stable equilibrium states are solved, and the dynamic stochastic evolution characteristics of advanced remanufacturing technology are revealed. Finally, an example is given to illustrate the influence of the competitive degree of online and offline recyclers and the price sensitivity coefficient of consumer recycling on the member equilibrium strategy and profit under two equilibrium conditions. The results show that increasing the advanced remanufacturing technology can effectively reduce the direct recovery price and transfer recovery price. Due to the influence of random disturbance, the advanced level of remanufacturing technology always fluctuates up and down around its expectation, and finally stabilizes to a steady-state value with time. Competition between online and offline recyclers can encourage remanufacturers to invest more in innovation efforts to improve the overall remanufacturing rate of the electronic waste, but it will reduce the Recycler's unit profit level, and excessive competition is not conducive to electronic waste recycling.