As public awareness of green environments grows and environmental protection regulations strengthen, the production and sales of environmentally friendly products have become crucial for traditional manufacturers. In this paper, we examine the pricing problem and coordination strategy between a manufacturer and a traditional retailer in a dual-channel supply chain of green products. The manufacturer sells both traditional and new green products through respective offline and online channels. Using a dynamic model to analyze the price game of the dual-channel supply chain, we investigate the effects of delay time lag, price adjustment speed, and green input level on the equilibrium price of the new green product. We obtain the Nash equilibrium point and stability region through the eigenvalue method and conduct numerical simulations. Our study shows that the trajectory of the product price evolution depends on system parameters, and that an optimal level of green input exists to maximize the manufacturer's profit. Our research emphasizes the importance of pricing strategies and coordination between manufacturers and retailers in the dual-channel supply chain of new green products. Overall, our findings provide valuable insights for traditional manufacturers seeking to leverage the growing demand for environmentally friendly products.