  We investigate the stability analysis of Schwarzschild black hole in
Einstein-scalar-Gauss-Bonnet (ESGB) theory because the instability of
Schwarzschild black hole without scalar hair implies the Gauss-Bonnet black
hole with scalar hair. The linearized scalar equation is compared to the
Lichnerowicz-Ricci tensor equation in the Einstein-Weyl gravity. It turns out
that the instability of Schwarzschild black hole in ESGB theory is interpreted
as not the tachyonic instability, but the Gregory-Laflamme instability of black
string. In the small mass regime of $1/\lambda<1.174/r_+$, the Schwarzschild
solution becomes unstable and a new branch of solution with scalar hair
bifurcates from the Schwarzschild one. This is very similar to finding a newly
non-Schwarzschild black hole in Einstein-Weyl gravity.
