Compared with other natural fibers, coir fiber has good strength characteristics and long-term anti-biodegradation ability. At present, most studies on randomly distributed coir fiber-reinforced soil have focused on cohesionless soil or granular soil. In this paper, the influence of randomly distributed coir fiber on the deviatoric stress and shear strength index of red clay with different fiber content was assessed by a consolidated undrained (CU) triaxial compression test. Since the hyperbolic variational character of the stress–strain relation of the samples conformed to the hyperbolic hypothesis of the Duncan–Chang model of nonlinear elastic model, the Duncan–Chang model was used to fit it, and the influences of fiber content and confining pressure on the parameters of the Duncan–Chang model were studied. The fiber content was determined by testing to be 0%, 0.2%, 0.25%, 0.3%, 0.35% and 0.4% of the dry soil mass. It has been found that coir fiber distributed in a random radial manner can significantly increase the deviatoric stress of red clay, and thus can be effectively used in the case of soil and fiber mixing. The cohesion of the red clay first increases and then decreases with the increase in fiber content, with an optimum content of 0.3%. The internal friction angle changes little with increasing fiber content.