We present long slit spectrophotometry of regions V and X of the local group irregular galaxy NGC 6822. The data consist of VLT FORS observations in the 3450 to 7500 A range. We have obtained electron temperatures and densities using different line intensity ratios. We have derived the He, C, and O abundances relative to H based on recombination lines, the abundance ratios among these elements are almost independent of the temperature structure of the nebulae. We have also determined the N, O, Ne, S, Cl, and Ar abundances based on collisionally excited lines, the ratios of these abundances relative to that of H depend strongly on the temperature structure of the nebulae. The chemical composition of NGC 6822 V is compared with those of the Sun, the Orion nebula, NGC 346 in the SMC, and 30 Doradus in the LMC. The O/H value derived from recombination lines is in good agreement with the value derived by Venn et al. (2001) from two A type supergiants in NGC 6822.