This paper addresses the optimal design of inter-plant hydrogen networks with intermediate headers of purity and pressure. A superstructure for inter-plant integration of hydrogen networks is presented, where all hydrogen sources and hydrogen sinks are indirectly matched with each other through intra-plant hydrogen headers and inter-plant hydrogen headers. The corresponding mathematical programming model is constructed and a tailored two-step strategy is proposed to solve the model. In this solving method, the topology of the inter-plant hydrogen network and the purity levels of the hydrogen headers are first determined to minimize the cost of hydrogen utilities. The placements of compressors and pressure levels of hydrogen headers are then optimized to reach the lowest total annual cost of the inter-plant hydrogen network. The application of the proposed method is illustrated via a practical industrial case of inter-plant hydrogen network in China. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.