We propose a method to generate an optical cage using azimuthal- and radial-variant vector beams in a high numerical aperture optical system. A new kind of vector beam that has azimuthal- and radial-variant polarization states is proposed and demonstrated theoretically. Then, an integrated analytical model to calculate the electromagnetic field and Poynting vector distributions of the input azimuthal- and radial-variant vector beams is derived and built based on the vector diffraction theory of Richards and Wolf. From calculations, a full polarization-controlled optical cage is obtained by simply tailoring the radial index of the polarization, the uniformity U of which is up to 0.7748, and the cleanness C is zero. Additionally, a perfect optical cage can be achieved with U=1, and C=0 by introducing an amplitude modulation; its magnetic field and energy flow are also demonstrated in detail. Such optical cages may be helpful in applications such as optical trapping and high-resolution imaging.