Multi-agent pickup and delivery (MAPD) is crucial in intelligent storage systems (ISSs), where multiple automated guided vehicles (AGVs) are assigned to various and potentially uncertain dynamic tasks. In this work, we consider a human–swarm hybrid system consisting of human workers and a swarm of AGVs collaborating to accomplish MAPD tasks. A human–swarm hybrid system pickup and delivery ((HS)$_{2}$PD) framework based on the receding-horizon prediction window is proposed, which facilities the development of future ISSs. This (HS)$_{2}$PD framework is essentially a two-layer hierarchical decision procedure, which takes the uncertainties of human behavior and the dynamic changes of tasks into account. The first layer is a two-level programming model handling the problems of mode assignment and task allocation. The second layer calculates each vehicle’s exact path by solving mixed-integer programmings. An integrated high-efficient algorithm for the (HS)$_{2}$PD problem is also proposed. The practicality and validity of the above algorithm are demonstrated via several groups of numerical simulations of (HS)$_{2}$PD tasks.