  We show the renormalization of contact interaction for odd-wave scattering in
one-dimension(1D). Based on the renormalized interaction, we exactly solve the
two-body problem in a harmonic trap, and further explore the universal
properties of spin-polarized fermions near odd-wave resonance using the
operator product expansion method. It is found that the high-momentum
distribution behaves as $C/k^2$, with $C$ the odd-wave contact. Various
universal relations are derived. Our work suggests a new universal system
emergent in 1D with large odd-wave scattering length.
