  In this paper, using the degeneration formula we obtain a blowup formulae of
local Gromov-Witten invariants of Fano surfaces. This formula makes it possible
to compute the local Gromov-Witten invariants of non-toric Fano surfaces form
toric Fano surface, such as del Pezzo surfaces. This formula also verifed an
expectation of Chiang-Klemm-Yau-Zaslow.
