Carbon fibers and catalyst for production of carbon fibers

Provided are carbon fibers with low metal ion elution amount without subjecting to high-temperature heat treatment, in which the metal ion may be sometimes precipitated on an electrode of electrochemical devices such as batteries and capacitors to cause short-circuit. The carbon fibers comprises Fe, at least one catalyst metal selected from the group consisting of Mo and V, and a carrier; wherein the carbon fibers have an R value (ID/IG) as measured by Raman spectrometry of 0.5 to 2.0 and have an electrochemical metal elution amount of not more than 0.01 % by mass.