We propose a polarization-insensitive design of a hybrid plasmonic waveguide (HPWG) optimized at the 3.392 μm wavelength which corresponds to the absorption line of methane gas. The waveguide design is capable of providing high mode sensitivity (Smode) and evanescent field ratio (EFR) for both transverse electric (TE) and transverse magnetic (TM) hybrid modes. The modal analysis of the waveguide is performed via 2-dimension (2D) and 3-dimension (3D) finite element methods (FEMs). At optimized waveguide parameters, Smode and EFR of 0.94 and 0.704, can be obtained for the TE hybrid mode, respectively, whereas the TM hybrid mode can offer Smode and EFR of 0.86 and 0.67, respectively. The TE and TM hybrid modes power dissipation of ~3 dB can be obtained for a 20-μm-long hybrid plasmonic waveguide at the 60% gas concentration. We believe that the highly sensitive waveguide scheme proposed in this work overcomes the limitation of the polarization controlled light and can be utilized in gas sensing applications.