Abstract: Accurate and reliable shielding calculation is an important component for ensuring the safety of nuclear devices. The discrete ordinates method is one of the most widely used deterministic transport calculation methods. For the shielding problem with strong angular flux anisotropy, insufficient precision of quadrature sets will lead to large discrete errors, which seriously affects the accuracy and reliability of shielding calculations. The linear and quadratic discontinuous finite element quadrature sets on regular icosahedron were constructed in the paper. The weights and directions of the quadrature sets were optimized to guarantee that the weights were strictly non-negative. The spherical harmonic function numerical integrations and IRI-TUB benchmark problem were used to verify the accuracy and adaptability of the quadrature sets. The numerical results show that linear discontinuous finite element quadrature sets on icosahedron can accurately integrate first-order and below spherical harmonic functions in one-twentieth spherical surface, and have fourth-order convergence. For IRI-TUB benchmark problem, the relative deviation between experimental measurement and calculation results is less than 25%. The adaptability and reliability of the discontinuous finite element quadrature sets on icosahedron in the practical shielding problem with strong angular flux density anisotropy are verified.