  We construct the holographic renormalization group (RG) flow of
thermo-electric conductivities when the translational symmetry is broken. The
RG flow is probed by the intrinsic observers hovering on the sliding radial
membranes. We obtain the RG flow by solving a matrix-form Riccati equation. The
RG flow provides a high-efficient numerical method to calculate the
thermo-electric conductivities of strongly coupled systems with momentum
dissipation. As an illustration, we recover the AC thermo-electric
conductivities in the Einstein-Maxwell-axion model. Moreover, in several
homogeneous and isotropic holographic models which dissipate the momentum and
have the finite density, it is found that the RG flow of a particular
combination of DC thermo-electric conductivities does not run. As a result, the
DC thermal conductivity on the boundary field theory can be derived
analytically, without using the conserved thermal current.
