Abstract: The radiation shielding design is an important part to ensure the safety of nuclear installations and the discrete ordinates method is one of main methods for shielding calculation. For shielding problems with long narrow gaps, the neutron angular flux distribution is highly anisotropic, especially highly forward-peaked in gaps. It is difficult to balance computational accuracy and efficiency for traditional discrete quadrature sets. A multi-level angular refinement technique for polar angle was developed based on Legendre-Chebyshev quadrature sets. The accuracy of low-order quadrature sets was enhanced on integrating angular flux by the refinement technique. Biased sets were also constructed to improve efficiency and asymptotic analyses about these sets were discussed. Seen from the results on the Kobayashi benchmark problem 2 of half scattering case, this technique can improve scalar flux accuracy in the gap.