The influences of the geometric deformation of the fiber such as ellipse, misalignment and diametrical nonuniformity on the performance of Orbital Angular Momentum (OAM) modes propagated in the Hollow Ring-core Polymer Optical Fiber (HRC-POF) are studied by full vector finite element method. In addition, the maximum deformation that the fiber can withstand under the condition that maintains the stable transmission of the OAM mode is also studied. The results show that the ellipse and misalignment will cause the mode walk-off upon propagation, leading to the decrease of the purity of synthesized OAM modes and the increase of the crosstalk. Numerical results show that the purity of synthesized OAM modes is more than 99.02% and the crosstalk is less than -20.08 dB when the ellipticity or misalignment is within 1.0%. The diametrical nonuniformity of the fiber will only affect the number of OAM modes supported in the HRC-POF. The larger the core radius is, the more OAM modes can be transmitted in the fiber. Besides, the original 26 OAM modes can be supported in HRC-POF when the diametrical nonuniformity is -3% to 10%.