In recent years, there has been a surge in the use of natural fiber polymer-based composites in various engineering fields due to their numerous advantages, including lower environmental pollution, ease of processing, high strength, and biodegradability. This study employed the Taguchi method to experimentally and statistically examine the effects of various fiber parameters on the tensile strength of a locally developed natural fiber-epoxy composite. The natural fiber used in the study was “Meriz,” a type of goat hair woven into the traditional Kurdish costume known as “Shall.” The fiber parameters examined included fiber orientation angles, weight fraction, form, and color. The results indicated that the tensile strength of the composite was improved by 100% when using the Meriz fiber with certain orientation angles, weight fraction, form, and colors, namely 0°/90°, 10 wt%, Shall, and brown, respectively. The analysis of variance also revealed that the fiber form had the most significant impact on tensile strength, contributing 40.74%. Confirmation testing demonstrated good agreement between the experimental and statistical data. Scanning electron microscopy was utilized to assess the interfacial bonding between the fiber reinforcement and the matrix and to analyze the fracture surface of the specimens with the highest and lowest tensile strength. The results indicated that the specimen with the highest tensile strength had excellent interfacial bonding compared to the specimen with the lowest tensile strength.