One option is to use the caption
package to define a ruled
style (adjust the settings to suit):
\documentclass{article}
\usepackage{caption}
\DeclareCaptionFormat{ruled}{
#1#2#3\par\vspace{-.65\baselineskip}\hrulefill\par\vspace{-.83\baselineskip}\hrulefill}
\captionsetup[table]{format=ruled}
\begin{document}
\begin{table}
\centering
\caption{Title}
\begin{tabular}{lc}
Stuff & More stuff
\end{tabular}
\end{table}
\end{document}
However, if your table begins with a horizontal rule, this might look odd.
If the double rules should be part of the tabular material, you can use for example booktabs
and its rule commands to define the double rule (in an example below I used \specialrule
to illustrate some control on the spacing requested in comment):
\documentclass{article}
\usepackage{caption}
\usepackage{booktabs}
\newcommand\doubleRule{\toprule\toprule}
\newcommand\doublerule{\toprule\specialrule{\heavyrulewidth}{\doublerulesep}{0.95em}}
\begin{document}
\begin{table}
\centering
\caption{A test table}
\begin{tabular}{l r}
\doubleRule
Header1 & Header2 \\
\midrule
Column1a & Column 2a \\
Column1a & Column 2a \\
\bottomrule
\end{tabular}
\end{table}
\captionsetup{skip=2pt}
\begin{table}
\centering
\caption{A test table}
\begin{tabular}{l r}
\doublerule
Header1 & Header2 \\
\midrule
Column1a & Column 2a \\
Column1a & Column 2a \\
\bottomrule
\end{tabular}
\end{table}
\end{document}