A reaction apparatus for producing vapor-grown carbon fibers (VGCF) and a continuous production system for producing VGCF are disclosed. The VGCF reaction apparatus is featured in installing a plurality of holes on the upper portion of inner tubes; and filling thermally conductive material in the areas between the inner tubes and the outer tube. The continuous production system includes the reaction apparatus, a product collection system and a carrier-gas collecting system, wherein carbon fibers produced by the reaction apparatus fall into the product collection system, and in the product collection system, a collection bin full-loaded with carbon fibers is pushed out and an empty bin is pushed into the collection chamber under PLC control as well as atmosphere replacement with inert gas, thereby continuously producing VGCF.