  The Max-Cut problem is known to be NP-hard on general graphs, while it can be
solved in polynomial time on planar graphs. In this paper, we present a
fixed-parameter tractable algorithm for the problem on `almost' planar graphs:
Given an $n$-vertex graph and its drawing with $k$ crossings, our algorithm
runs in time $O(2^k(n+k)^{3/2} \log (n + k))$. Previously, Dahn, Kriege and
Mutzel (IWOCA 2018) obtained an algorithm that, given an $n$-vertex graph and
its $1$-planar drawing with $k$ crossings, runs in time $O(3^k n^{3/2} \log
n)$. Our result simultaneously improves the running time and removes the
$1$-planarity restriction.
