The long-time trap and control of neutral atoms in an optical micro-cavity is a crucial problem in cavity quantum electrodynamics (QED), which greatly restricts the coherent manipulation of the interaction process between single atom and light. In this paper, we design a strongly coupled cavity QED system based on the traditional Fabry-Perot cavity. The parameters of the cavity are 3.5 millimeters in length, about 57000 in fineness, (g0,,)=2 (1.48, 0.375, 2.61) MHz, 1.54 and 0.89 in critical photon and atom number, respectively. The system allows building the magneto-optical trap (MOT) and optical lattice directly inside the cavity, which provides the possibility of long-time trapping deterministic single neutral atom or a number of neutral atoms in the cavity. By setting up a dipole trap and atomic imaging system, the capture, detection and imaging of single atom or several atoms in the cavity can be realized. The system overcomes some difficulties in transferring atoms in the usual cavity QED and has potential applications in robust intracavity atom control for quantum information processing.