Although the inter-layer coupling in layered materials has attracted considerable interest due to its importance in determining physical properties of two-dimensional systems, studies on the inter-layer coupling in one-dimensional systems have so far been limited. Double-wall carbon nanotubes (DWCNTs) are one of the most fundamental and ideal model systems to study the inter-layer coupling in one-dimensional systems. In this work, Rayleigh scattering spectroscopy and transmission electron microscopy are used to characterize the electronic transition between inner-and outer-nanotubes of the exactly same individual DWCNT. We find that the inter-layer coupling is strong, leading to downshifts in most of the optical transition energies (up to similar to 0.2 eV) compared to isolated CNTs. We also find that the presence of metallic tubes lead to stronger shifts. The inter-layer screening of Coulomb interactions is one of the key factors in explaining the observed results.