We establish some
Φ
\Phi
-moment inequalities for noncommutative differentially subordinate martingales. Let
Φ
\Phi
be a
p
p
-convex and
q
q
-concave Orlicz function with
1
>
p
≤
q
>
2
1>p\leq q>2
. Suppose that
x
x
and
y
y
are two self-adjoint martingales such that
y
y
is weakly differentially subordinate to
x
x
. We show that, for
N
≥
0
N\geq 0
,
τ
[
Φ
(
|
y
N
|
)
]
≤
c
p
,
q
τ
[
Φ
(
|
x
N
|
)
]
,
\begin{equation*} \tau \big [\Phi (|y_N|)\big ]\leq c_{p,q}\tau \big [\Phi (|x_N|)\big ], \end{equation*}
where the constant
c
p
,
q
c_{p,q}
is of the best order when
p
=
q
p=q
. The
Φ
\Phi
-moment estimates for square functions of noncommutative differentially subordinate martingales are also obtained in this article. Our approach provides constructive proofs of noncommutative
Φ
\Phi
-moment Burkholder–Gundy inequalities and Burkholder inequalities.