Tl2Mo6Se6 composed of quasi-one-dimensional (quasi-1D) (Mo6Se6) chains oriented along the z-axis, weakly coupled by Tl ions, giving them pseudo-one-dimensional character. Tl2Mo6Se6 is superconducting with a Tc o 3 K- 6.5 K (varies between samples) and has the greatest uniaxial anisotropy, comparable to the most anisotropic organic superconductors, albeit very simple band structures on the Fermi surface. Moreover, quasi-one-dimensional Tl2Mo6Se6 compound has also been identified as the possible candidate that can support the rare cubically dispersed Dirac semimetal and predicted for time-reversal invariant spin-triplet topological superconductivity. All these exotic features make Tl2Mo6Se6 an ideal candidate to study unconventional topological superconductivity. Here we propose to study the superconducting ground state properties of Tl2Mo6Se6 by muon spin relaxation/rotation measurements.