We investigate
N
2
+
air lasing at 391 nm, induced by strong laser fields in a nitrogen glow discharge plasma. We generate forward
N
2
+
air lasing on the
B
2
Σ
u
+
(
v
′
=
0
)
–
X
2
Σ
g
+
(
v
″
=
0
)
transition at 391 nm by irradiating an intense 35-fs, 800-nm laser in a pure nitrogen gas, finding that the 391-nm lasing quenches when the nitrogen gas is electrically discharged. In contrast, the 391-nm fluorescence measured from the side of the laser beam is strongly enhanced, demonstrating that this discharge promotes the population in the
B
2
Σ
u
+
(
v
′
=
0
)
state. By comparing the lasing and fluorescence spectra of the nitrogen gas obtained in the discharged and laser-induced plasma, we show that the quenching of
N
2
+
lasing is caused by the efficient suppression of population inversion between the
B
2
Σ
u
+
and
X
2
Σ
g
+
states of
N
2
+
, in which a much higher population occurs in the
X
2
Σ
g
+
state in the discharge plasma. Our results clarify the important role of population inversion in generating
N
2
+
air lasing, and also indicate the potential for the enhancement of
N
2
+
lasing via further manipulation of the population in the
X
2
Σ
g
+
state in the discharged medium.