A dual-channel recycling model is built to describe price competition between qualified platform of online recycling and unqualified recyclers in two channels which have different e-waste disposal approaches. We take environmental awareness of two types of consumers into consideration in this model and use game theory to compare the decision-making of two channels in the situation of competition and cooperation respectively. The research shows that the environmental awareness of consumers and the proportion of environmental consumers have different effects on the cooperation strategy of the two channels in different market environment. Under cooperative scenario, the profit of the supply chain increases with the environmental awareness of consumers, and decreases with the proportion of environmental consumers. In general, the recycling price and the recycling amount in cooperative scenario are less than that in competitive scenario, except that unit profits of recycled products of the platform is too high. When the environmental awareness of consumers, the proportion of environmental consumers and the unit profit of recycled products of two channels meet some certain conditions, the cooperation strategy has a positive effort on the whole industry. The impact of exogenous parameters on the model of supply chain is discussed, and numerical examples are given to verifly the effectiveness of the model.