  We study static non-critical hairy black holes of four dimensional
gravitational model with nonminimal derivative coupling and a scalar potential
turned on. By taking an ansatz, namely, the first derivative of the scalar
field is proportional to square root of a metric function, we reduce the
Einstein field equation and the scalar field equation of motions into a single
highly nonlinear differential equation. This setup implies that the hair is
secondary-like since the scalar charge-like depends on the non-constant
mass-like quantity in the asymptotic limit. Then, we show that near boundaries
the solution is not the critical point of the scalar potential and the
effective geometries become spaces of constant scalar curvature.
