© The Institution of Engineering and Technology.This study is a step forward to introduce the new fundamentals of LC infinite rectangle circuit network in the fractional domain. The authors first derive the general formula of the impedance between two arbitrary nodes of the fractional-order infinite rectangle circuit network by using Fourier transform in a coordinate system. Then, two properties (relevance and symmetry) of the fractional-order circuit network are systematically discussed. On the basis of these findings, the impedance can also be derived. Moreover, a comparative analysis is carried out to show an excellent agreement between the results obtained here and the results of the previous studies. Furthermore, the effects of the system parameters on the impedance characteristics and phase characteristics are systematically discussed. Finally, four potential application cases are presented. Numerical simulations are presented to verify the theoretical results introduced.