  A natural broad energy germanium (BEGe) detector is operated in the China
Jinping Underground Laboratory (CJPL) for a feasibility study of building the
next generation experiment of the neutrinoless double-beta (0{$\nu\beta\beta$})
decay of $^{76}$Ge. The setup of the prototype facility, characteristics of the
BEGe detector, background reduction methods, and data analysis are described in
this paper. A background index of 6.4$\times$10$^{-3}$
counts/(keV$\cdot$kg$\cdot$day) is achieved and 1.86 times lower than our
previous result of the CDEX-1 detector. No signal is observed with an exposure
of 186.4 kg$\cdot$day, thus a limit on the half life of $^{76}$Ge
0$\nu\beta\beta$ decay is set at T$_{1/2}^{0\nu}$ $>$ 5.62$\times$10$^{22}$ yr
at 90% C.L.. The limit corresponds to an effective Majorana neutrino mass in
the range of 4.6 $\sim$ 10.3 eV, dependent on the nuclear matrix elements.
