In this article, we focus on human-to-cobot dual-arm handover operations for large box-type objects. The efficiency of handover operations should be ensured and the naturalness as if the handover is going on between two humans. First of all, we study the human-human dual-arm large box-type object natural handover process to guide this research. Then, for efficiency, we combine the probabilistic approach with the online learning algorithm to predict the beginning of the handover task and handover positions. The online updating probabilistic models can deal with not only human givers' regular motion patterns but also their irregular motion patterns. Then, to guarantee that human givers can perform handover operations naturally, we apply the probabilistic robot skill learning method kernelized movement primitives (KMPs) to adapt the learned receiving skills and fulfill some constraints for safety based on online predicted results. Furthermore, we give special attention to the dual-arm grasp strategy and control design to guarantee a stable grasp. In addition, we equip this handover system on a Baxter cobot and extend its grippers to make it more suitable for dual-arm handover operations. The experimental results show that the proposed handover system can solve human-to-cobot dual-arm handover operations for large box-type objects naturally and efficiently.