Due to low density and low coefficient of thermal expansion, orthotropic materials, namely, the polymer matrix composites are finding their way in many of the engineering application. The present study reports the performance of an orthotropic annular fin with material response of polymer matrix composites. The thermal conductivity along radial and axial direction is governed by the thermal conductivity ratio (K), which is an important parameter for orthotropic annular fin. The work then numerically examines in two dimensions, the thermal performance of the annular fin at different thermal conductivity ratio (K) for the rectangular profile using the finite difference method. Different convective heat transfer coefficient are considered at the fin sides and the fin tip. The effect of various parameters such as axial Biot number (Bi_s), contact Biot number (Bi_c), tip Biot number (Bi_e), aspect ratio (b/a), thermal conductivity ratio (K) on the efficiency (Η) and temperature distribution over the fin surface are presented.