Calibration-free laser induced breakdown spectroscopy (CF-LIBS) was used for the determination of elemental composition and quantitative analysis of the Košice meteorite by means of time resolved and broadband emission spectroscopy (200–1000 nm). The electron temperature was determined using the Saha-Boltzmann plot method and the electron density from Stark broadening of the hydrogen Hα line (656 nm). Apart from magnesium, silicon and iron, which are the main elemental constituents of examined meteorite fragments, elements such as aluminum, nickel, potassium, sodium, chromium, calcium and manganese were also identified in the obtained LIBS spectra. Concentrations of Al, Ca, Cr, Fe, Mg, Mn, Na, Ni and Si were calculated using the calibration free approach and results were compared with ones obtained from the ICP-MS analyses. For the increase of the CF-LIBS accuracy, a selection of spectral lines was performed. Considering the transition probability, the population of absorbing level, the degree of ionization and predicted elemental concentration we calculated the probability of self-absorption and, consequently, spectral lines with highest self-absorption probability were rejected. CF-LIBS can be used as an alternative method for the meteorite fragments analysis (including the inner part and crust), because this method is quasi non-destructive and therefore analysis of all found fragments with minimal destruction is possible.