Surface rippling may appear in ductile polymer nanofibers under axial stretching. Such rippling phenomenon has been detected in as-electrospun polyacrylonitrile (PAN) in recent single-fiber tension tests and in electrospun polyimide (PI) nanofibers after imdization. We herein propose a simple one-dimensional (1D) nonlinear elastic model to take into account the combined effect of surface tension and nonlinear elasticity during the rippling initiation and its evolution in compliant polymer nanofibers. The polymer nanofiber is modeled as incompressible, isotropically hyperelastic Mooney-Rivlin solid. The fiber geometry prior to rippling is considered as a long circular cylinder. The governing equation of surface rippling is established through linear perturbation of the static equilibrium state of the nanofiber subjected to finite axial pre-stretching. Critical stretch and ripple wavelength are determined in terms of surface tension, elastic property, and fiber radius. Numerical examples are demonstrated to examine these dependencies. Besides, a critical fiber radius is determined, below which the polymer nanofibers are intrinsically unstable. The present model, therefore, is capable of predicting the rippling condition in compliant nanofibers, and can be further used as continuum mechanics approach for the study of surface instability and nonlinear wave propagation in compliant fibers and wires at nanoscale.