In this paper, a coordinated production and transportation scheduling problem on two-machine flow-shop is studied. After being processed on the first machine, the jobs are transported to the second machine in batches by a transporter with capacity limitation. Each job has different size requirement during transportation. The objective is to minimize the maximum makespan. Since different jobs belonged to different customers have the competition for the machines and the transporter, a non-cooperative game model is established. In this game model, the jobs are viewed as players, the waiting time of each job is viewed as the strategy, and the completion time of each job is viewed as its profit. By transforming the problem into a Markov decision process, a Q-learning algorithm with linear approximate value function is designed to solve Nash equilibrium scheduling. The experimental results show that the approximate Nash equilibrium scheduling obtained by Q-learning algorithm has a better global optimality. The algorithm can improve the production efficiency and achieve a win-win situation for customers and enterprises in satisfying with the interests of customers.