  A matching of a graph is a set of edges without common end vertex. A graph is
called 1-planar if it admits a drawing in the plane such that each edge is
crossed at most once. Recently, Biedl and Wittnebel proved that every 1-planar
graph with minimum degree 3 and $n\geq 7$ vertices has a matching of size at
least $\frac{n+12}{7}$, which is tight for some graphs. They also provided
tight lower bounds for the sizes of matchings in 1-planar graphs with minimum
degree 4 or 5. In this paper, we show that any 1-planar graph with minimum
degree 6 and $n \geq 36$ vertices has a matching of size at least
$\frac{3n+4}{7}$, and this lower bound is tight. Our result confirms a
conjecture posed by Biedl and Wittnebel.
