The controllability of the linearized KdV equation with right Neumann control is studied in the pioneering work of Rosier [L. Rosier, ESAIM: COCV 2 (1997) 33-55.]. However, the proof is by contradiction arguments and the value of the observability constant remains unknown, though rich mathematical theories are built on this totally unknown constant. We introduce a constructive method that gives the quantitative value of this constant.