In biological tissues, collagen type I usually works in the form of crimped fibers, showing a special mechanical nonlinearity namely strain hardening. The nonlinearity enables the biological tissues to functionalize with low modulus at lower strain and protects the damage of tissues by hypernomic strain with high modulus at higher strain. In order to mimic the nonlinear elasticity of collagen type I fibers, fiber membranes of a biodegradable material PLCL were prepared by electrospinning, subsequently the effects of pre-stretching were introduced to increase fiber alignment and the stress in a single nanofiber, and plasticizer and heat treatment was applied to relax the residual stress in the nanofibers for produce crimped fiber structure. The effects of heating temperature, pre-stretching and fixed contraction were investigated to obtain controllable crimped structures of electrospun nanofibers. The results suggested that the degree of crimpness increased with the increasing orientation degree of the fiber and the heat treatment temperature. Moreover, the decreased fixed-contraction length provided larger degrees of freedom for the formation of crimped structure. A phenomenological hyperelastic mathematical model was employed to describe the mechanical nonlinearity of the crimped fibers, the corresponding characteristic parameters were obtained and their physical significance were discussed. The curve fitting results indicated that the characteristic parameter A of the model is highly related to the initial slope of the stress-strain curve, and the B value changes in line with the crimpness of the fibers. These results suggests that fiber membrane with a controllable crimped structure and nonlinear elasticity is able to be implemented by tuning the processing conditions, which has a extensively potential for the repair of tendons, soft connective tissue, and the construction of tissue engineering vascular scaffold