The present paper presents an auto-focus laser-induced breakdown spectroscopy (LIBS) remote measuring system. This system contains a Schwarzschild telescope, which consists of a convex mirror and a concave mirror. The two spherical mirrors are coaxially placed. The convex mirror is mounted on a motorized linear translation stage. With this motorized linear translation stage, the convex mirror can move along the optical axis to change the spacing between the convex mirror and the concave mirror. Therefore the focal length can be adjusted to focus the laser on samples at different distances and collect the plasma spectra. The advantages of the telescope system include, firstly, the light path of laser focusing and spectra signal collection is the same, which make it easier for mounting and collimation;secondly, the light path of the telescope uses total reflection type, which is fit for the detection in ultra-violate region;finally, the telescope consists of only two spherical mirrors which are relatively easier to manufacture. Within the translation range of the motorized linear translation stage, the focal length of the telescope in this paper can be adjusted from 1.5 to 3.6 m. The diameter of the focusing spot varies from 0.5 to 1.0 mm. Utilizing this telescope system, LIBS experiments were conducted using copper sample. And the characteristic lines of Cu element (Cu Ⅰ 223.01 nm, Cu Ⅰ 224.43 nm) obtained are used for the auto focusing. By investigating the relation of the area of spectral lines covered and the spacing between the mirrors, the optimal laser focusing location was obtained .The LIBS experiment results show that the system functions well, fulfilling the demand of remote ablation of sample and LIBS spectral measuring, and the telescope is able to auto-focus the laser on samples at different position to perform remote LIBS experiment.