The present study proposes a modified random sequential absorption (RSA) algorithm to generate a representative volume element (RVE) model for predicting the elastic properties of discontinuous curved fiber reinforced composites (DCFRCs) with varying fiber waviness functions and orientations. A small-move method was proposed to modify the traditional RSA algorithm. In comparison with the original RSA algorithm, the generation efficiency of the proposed modified RSA algorithm increased by over 40%, and the achievable maximum fiber volume fraction could reach up to 15% with a fiber aspect ratio of 15. The generated RVE model was utilized in conducting finite element analysis to investigate the effect of fiber waviness and wavy functions on the elastic properties of DCFRCs. Finally, a modified rule-of-mixture was proposed to predict the elastic properties of DCFRCs with various fiber orientations. The results indicated that the elastic properties predicted by the modified rule-of-mixture were in good agreement with those obtained from the RVE model, thereby demonstrating its effectiveness.