Here's one possibility using \colorbox
and a \parbox
:
\documentclass{moderncv}
\moderncvtheme{classic}
\firstname{John}
\familyname{Doe}
\makeatletter
\renewcommand*{\sectionstyle}[1]{\colorbox{color1}{%
\parbox[t]{\dimexpr\textwidth-2\fboxsep\relax}{\sectionfont#1}}}
\renewcommand*{\section}[1]{%
\par\addvspace{2.5ex}%
\phantomsection{}% reset the anchor for hyperrefs
\addcontentsline{toc}{section}{#1}%
\strut\sectionstyle{#1}%
\par\nobreak\addvspace{1ex}\@afterheading}
\makeatother
\begin{document}
\makecvtitle
\section{CORE COMPETENCIES}
\end{document}

Perhaps this modification follows more accurately the image in the question (no horizontal space between the colored box and the text and bold-faced text); I also added \MakeUppercase
to \sectionstyle
:
\documentclass{moderncv}
\moderncvtheme{classic}
\firstname{John}
\familyname{Doe}
\makeatletter
\renewcommand\sectionfont{\bfseries\large}
\renewcommand*{\sectionstyle}[1]{{%
\setlength\fboxsep{0pt}%
\colorbox{color1}{%
\parbox[t]{\textwidth}{\sectionfont\rule[-.5ex]{0pt}{2.8ex}\MakeUppercase{#1}}}}}
\renewcommand*{\section}[1]{%
\par\addvspace{2.5ex}%
\phantomsection{}% reset the anchor for hyperrefs
\addcontentsline{toc}{section}{#1}%
\sectionstyle{#1}%
\par\nobreak\addvspace{1ex}\@afterheading}
\makeatother
\begin{document}
\makecvtitle
\section{Core competencies}
\end{document}

Your posted code produces this:

Check your log file, it appears that you do not have the marvosym fonts installed.
Best Answer
This is a duplication using the
article
class and some formatting: