A characterization of
P
P
-convexity of arbitrary Banach space is given. Moreover, it is proved that the Orlicz-Bochner function space
L
L
Φ
(
μ
,
X
)
_\Phi (\mu ,X)
is P-convex if and only if both spaces
L
Φ
(
μ
)
L_\Phi (\mu )
and
X
X
are
P
P
-convex. In particular, the Lebesgue-Bochner space
L
p
(
μ
,
X
)
L^p(\mu ,X)
with
1
>
p
>
∞
1>p>\infty
is
P
P
-convex iff
X
X
is
P
P
-convex.