Process planning and job shop scheduling problems are the two classical but crucial activities in manufacturing system. With the approach of integrated process planning and scheduling, the two actual activities are combined to conduct operation selection and operation sequencing with the constraints of practical job shop status. In this article, a quantum-inspired hybrid algorithm with the objective of minimum makespan is proposed, aiming to solve integrated process planning and scheduling problems in dynamic manufacturing systems. A hybrid-coding representation is suggested, which is a three-layer structure in numerical representation and Q-bit representation adopted from quantum-inspired evolutionary algorithm. Based on the hybrid-coding representation, customized converting and repairing rules and methods are presented to generate feasible individuals. Q-gate rotation and group leader optimization algorithm are integrated systematically for the population evolution to accelerate the convergence speed of the proposed algorithm. In order to increase the diversity of population, a chaotic map called logistic map is introduced, bringing the stochastic initial individuals. Experiments show that the proposed hybrid algorithm can generate outstanding outcomes for integrated process planning and scheduling instances.