Although comprehensive progress has been made in the area of coordination polymer (CP)/metal-organic framework (MOF)-based proton-conducting materials over the past decade, searching for a CP/MOF with stable, intrinsic, high anhydrous proton conductivity that can be directly used as a practical electrolyte in an intermediate-temperature proton-exchange membrane fuel cell assembly for durable power generation remains a substantial challenge. Here, we introduce a new proton-conducting CP, (NH4)3[Zr(H2/3PO4)3] (ZrP), which consists of one-dimensional zirconium phosphate anionic chains and fully ordered charge-balancing NH4+ cations. X-ray crystallography, neutron powder diffraction, and variable-temperature solid-state NMR spectroscopy suggest that protons are disordered within an inherent hydrogen-bonded infinite chain of acid-base pairs (N-H···O-P), leading to a stable anhydrous proton conductivity of 1.45 × 10-3 S·cm-1 at 180 °C, one of the highest values among reported intermediate-temperature proton-conducting materials. First-principles and quantum molecular dynamics simulations were used to directly visualize the unique proton transport pathway involving very efficient proton exchange between NH4+ and phosphate pairs, which is distinct from the common guest encapsulation/dehydration/superprotonic transition mechanisms. ZrP as the electrolyte was further assembled into a H2/O2 fuel cell, which showed a record-high electrical power density of 12 mW·cm-2 at 180 °C among reported cells assembled from crystalline solid electrolytes, as well as a direct methanol fuel cell for the first time to demonstrate real applications. These cells were tested for over 15 h without notable power loss.