The coexistence of high electron conduction and low heat conduction are essentially important to realize efficient thermal management materials such as thermoelectric materials. Although introducing 0D point defects (Fig. a) or 2D layers (Fig. c) is known as an effective way to reduce the heat conduction, there is a dilemma that the electron conduction is also reduced due to that electrons and phonons are scattered simultaneously by impurities, defects, and boundaries. Here we show that introducing a 1D atomic defect tunnel is an excellent solution to solve this dilemma. (Fig. b) In this structure, the probability of that phonon hits the 1D atomic defect tunnel or wire is much higher than that of introducing 0D defect or dot event though 1D defect density is low. In order to verify this hypothesis experimentally, we selected oxygen deficient tungsten oxide epitaxial film as the candidate material. The WO x films (2.7 < x < 3.0) were heteroepitaxial grown by the pulsed laser deposition technique on (001) and (110) LaAlO3 single crystal substrates under oxygen atmosphere. The oxygen pressure was precisely controlled from 2 to 13 Pa during the deposition. As a result, we found that 1D atomic defect tunnels can be introduced in tungsten oxide epitaxial films by oxygen removal. In order to visualize the atomic arrangement of the WO x films, high-angle annular dark-field (HADDF) scanning transmission electron microscopy (STEM) was performed. The resultant WO x epitaxial films contain 1D atomic defect tunnel in the in-plane direction and the density increased with decreasing x. The thermal conductivity (κ) of the films drastically decreased from ~7 W m-1 K-1 to ~1.5 W m-1 K-1 in order to minimize κ with increasing 1D defects. The κ values of WO x films are close to that of amorphous WO x , which shows minimum κ. On the other hand, the electrical conductivity (σ) in the in-plane direction of WO x film dramatically increased from ~10-1 S cm-1 to ~103 S cm-1. Since the oxygen removal reduces the valence state of tungsten, carrier electron concentration increases with increasing 1D defects. The introduction of 1D defect tunnels does not affect the electron propagation but selectively suppresses only the phonon propagation most likely due to the fact that mean free path is much shorter for the carrier electron compared to the phonon. Thus, high electron conduction and low heat conduction coexist in oxygen-deficient tungsten oxide epitaxial films. The present finding would be useful to design efficient thermal management materials such as thermoelectric materials. Figure 1