Electrospun polymer nanofibers have garnered significant interest due to their strong size-dependent material properties, such as tensile moduli, strength, toughness, and glass transition temperatures. These properties are closely correlated with polymer chain dynamics. In most applications, polymers usually exhibit viscoelastic behaviors such as stress relaxation and creep, which are also determined by the motion of polymer chains. However, the size-dependent viscoelasticity has not been studied previously in polymer nanofibers. Here, we report the first experimental evidence of significant size-dependent stress relaxation in electrospun Nylon-11 nanofibers as well as size-dependent viscosity of the confined amorphous regions. In conjunction with the dramatically increasing stiffness of nano-scaled fibers, this strong relaxation enables size-tunable properties which break the traditional damping-stiffness tradeoff, qualifying electrospun nanofibers as a promising set of size-tunable materials with an unusual and highly desirable combination of simultaneously high stiffness and large mechanical energy dissipation. Published by AIP Publishing.