  Ovadia and Rodriguez-Hertz \cite{OH} defined the neutralized Bowen open ball
as $$B_n(x,e^{-n\varepsilon}) = \{y\in X:d(T^j(x),T^j(y)) < e^{-n\varepsilon},
\forall 0\leq j\leq n-1\}.$$ Yang, Chen and Zhou \cite{YCZ} introduced the
notion of neutralized Bowen topological entropy of subsets by replacing the
usual Bowen ball by neutralized Bowen open ball. And they established
variational principles for this notion. In this note, we extend this result to
the non-additive neutralized Bowen topological pressure and established the
variational principle for non-additive potentials with tempered distortion.
