Potassium-ion　batteries　are　a　promising　alternative　to　lithium-ion　batteries.　However,　it　is　challenging　to　achieve　fast　charging/discharging　and　long　cycle　life　with　the　current　electrode　materials　because　of　the　sluggish　potassiation　kinetics.　Here　we　report　a　soft　carbon　anode,　namely　highly　nitrogen-doped　carbon　nanofibers,　with　superior　rate　capability　and　cyclability.　The　anode　delivers　reversible　capacities　of　248　mAh　g(-1)　at　25　mA　g(-1)　and　101　mAh　g(-1)　at　20　A　g(-1),　and　retains　146　mAh　g(-1)　at　2　A　g(-1)　after　4000　cycles.　Surface-dominated　K-storage　is　verified　by　quantitative　kinetics　analysis　and　theoretical　investigation.　A　full　cell　coupling　the　anode　and　Prussian　blue　cathode　delivers　a　reversible　capacity　of　195　mAh　g(-1)　at　0.2　A　g(-1).　Considering　the　cost-effectiveness　and　material　sustainability,　our　work　may　shed　some　light　on　searching　for　K-storage　materials　with　high　performance.