Let
L
=
−
Δ
+
μ
be the generalized Schrödinger operator on
ℝ
d
,
d
≥
3
,
where
μ
≠
0
is a nonnegative Radon measure satisfying certain scale-invariant Kato conditions and doubling conditions. In this work, we give a new
BMO
space associated to the generalized Schrödinger operator
L
,
BM
O
θ
,
L
, which is bigger than the
BMO
spaces related to the classical Schrödinger operators
A
=
−
Δ
+
V
, with
V
a potential satisfying a reverse Hölder inequality introduced by Dziubański et al. in 2005. Besides, the boundedness of the Littlewood-Paley operators associated to
L
in
BM
O
θ
,
L
also be proved.