Let
N
=
L
∞
(
G
m
)
⊗
¯
M
\mathcal {N}=L_{\infty }(G_{\mathbf {m}})\bar {\otimes }\mathcal {M}
where
M
\mathcal {M}
is a semifinite von Neumann algebra and
G
m
G_{\mathbf {m}}
is a bounded Vilenkin group. Considering the partial sums
S
n
(
f
)
S_n(f)
of the Vilenkin-Fourier series of
f
∈
L
1
(
N
)
f\in L_1(\mathcal {N})
, we prove that there is a universal constant
c
c
independent of
f
f
,
n
n
and
M
\mathcal {M}
such that
‖
S
n
(
f
)
‖
L
1
,
∞
(
N
)
≤
c
‖
f
‖
L
1
(
N
)
.
\begin{equation*} \|S_n(f)\|_{L_{1,\infty }(\mathcal {N})}\leq c\|f\|_{L_1(\mathcal {N})}. \end{equation*}
Consequently, by transference argument, we obtain Scheckter and Sukochev’s result in the noncommutative bounded Vilenkin system setting. We also show the
H
1
H_1
-
L
1
L_1
boundedness for modified partial sums.