In this paper, we give a positive answer to the question raised in Kosiński (Complex Anal Oper Theory 9(6):1349–1359, 2015) and Zapałowski (J Math Anal Appl 430(1):126–143, 2015), i.e., we show that the pentablock$${\mathcal {P}}$$
P
is a $${\mathbb {C}}$$
C
-convex domain.