High gravimetric energy density and volumetric energy density energy storage devices are highly desirable due to the rapid development of electric vehicles, and portable and wearable electronic equipment. Electrospinning is a promising technology for preparing freestanding electrodes with high gravimetric and volumetric energy density. However, the energy density of the traditional electrospun electrodes is restricted by the low mass loading of active materials (e.g. 20%-30 wt%). Herein, a biomimetic strategy inspired by the phenomenon of the sticky spider web is demonstrated as a high performance anode, which simultaneously improves the gravimetric and volumetric energy density. Freestanding carbon nanofiber (CNF) membranes containing over 50 wt% of bismuth were prepared by electrospinning and subsequent thermal treatment. Membranes consisting of CNF network structures bonded tightly with active Bi cluster materials, resulting in excellent mechanical protection and a fast charge transport path, which are difficult to achieve simultaneously. The composite membrane delivers high reversible capacity (483 mA h g-1 at 100 mA g-1 after 200 cycles) and high rate performance (242 mA h g-1 at 1 A g-1) as a lithium-ion battery anode. For use as a sodium ion battery, the composite membrane also shows a high reversible specific capacity of 346 mA h g-1 and outstanding cycling performance (186 mA h g-1 at 50 mA g-1 after 100 cycles). This work offers a simple, low cost and eco-friendly method for fabricating free-standing and binder-free composite electrodes with high loading used in LIBs and SIBs.