  In \cite{WeiWu22-3} (J.Geom.Anal.32, 199(2022)), we classified HCMU surfaces
in 3-dimensional Euclidean space as Weingarten surfaces by holomorphic
functions. In this paper, using a totally different method from
\cite{WeiWu22-3}, we will classify HCMU surfaces in 3-dimensional space forms
as Weingarten surfaces. Moreover we will give a criteria of a Weingarten
surface which is also an HCMU surface.
