A new f(R) black hole

f(R) gravity is a straight extension of general relativity,in which the Lagrangian is an arbitrary function of the curvature scalar R.We derive an exact spherically symmetric vacuum solution to the field equations of the metric f(R) gravity with the condition F(r)=1+αr (F(r)≡(df(R(r)))/(dr) and the term αr indicates a minor correction to general relativity).Moreover,we consider the scalar perturbations on this black hole background spacetimes.Using the six-order WKB (Wentzel-Kramers-Brillouin) method,we discuss the relations between quasinormal modes of this black hole and its parameters which show that the black hole is stable