Purpose: To examine and compare peri-implant bone stress under the occlusal forces of 30% carbon fiber–reinforced polyetheretherketone (Cfr-PEEK), 60% Cfr-PEEK, and titanium (Ti) materials for dental implants through finite element analysis (FEA). Materials and Methods: Single-tooth implants made of 30% Cfr-PEEK, 60% Cfr-PEEK, and Ti were modeled in the maxillary anterior, maxillary posterior, and mandibular posterior regions. As a result of the applied vertical and oblique forces, von Mises stresses—including the maximum principal stress values, minimum principal stress values, and stress distributions in the implant—in the cortical bone and cancellous bone of each model were examined. Results: Overall, 30% Cfr-PEEK implants’ stress in the surrounding bone was higher than that in the Ti and 60% Cfr-PEEK implants. The 60% Cfr-PEEK material displayed a lower stress distribution on both cortical and cancellous peri-implant bone in all models. Conclusions: Ti and 60% Cfr-PEEK implants were found to distribute stresses to bone more homogeneously than the 30% Cfr-PEEK implants. Overall, oblique forces had a more destructive effect than vertical forces, and denser bone structures showed better stress distribution against incoming forces.