In this brief note, we investigate the
C
P
2
\mathbb {CP}^2
-genus of knots, i.e., the least genus of a smooth, compact, orientable surface in
C
P
2
∖
B
4
˚
\mathbb {CP}^2\smallsetminus \mathring {B^4}
bounded by a knot in
S
3
S^3
. We show that this quantity is unbounded, unlike its topological counterpart. We also investigate the
C
P
2
\mathbb {CP}^2
-genus of torus knots. We apply these results to improve the minimal genus bound for some homology classes in
C
P
2
#
C
P
2
\mathbb {CP}^2\# \mathbb {CP} ^2
.