The p-wave superfluid state is a promising spin-triplet and non s-wave pairing state in an ultracold Fermi gas. In this work we study the low-temperature shear viscosity of a one-component p-wave superfluid Fermi gas, by means of Kubo formalism. Our study is done in the strong-coupling limit where Fermi superfluid reduces into a system of composite bosons. Taking into account px-wave Cooper channel in the self-energy, the viscous relaxation rates are determined. The relaxation rates related to these interactions are calculated as a function of temperature. Their temperature dependence is different from the s-wave superfluid Fermi gas, and this is due to the anisotropic pairing interaction in the p-wave superfluid. Our results contribute to understand how this anisotropy affects transport properties of this unconventional superfluid Fermi gas in low temperature limit.