We present a systematic and comparative study of the electronic properties of CeX monochalcogenides, The density of state (DOS) and electronic band structure of CeX (X=S, Se, Te) have been calculated using the full-potential linearized augmented plane-wave (FP-LAPW) + local orbital (lo) method based on the density functional theory (DFT), which is implemented in WIEN2k code. The trends in the high pressure behavior of these systems are discussed. Four approximations for the exchange-correlation functional have been used, the GGA's of Perdew-Burke-Ernzherhof. (PBE08), Engel-Vosko (EV93), a modified version of the exchange potential proposed by Becke and Johnson (MBJ), and LDA+U is used to calculate the band gaps at different pressures. All methods allow for a description of the Ce f electrons as either localized or delocalized, it is found that the underestimations of the bandgap by means of LDA- GGA and Engel-Vosko are considerably improved by using the modified Becke-Johnson (MBJ) potential for all compounds in the series, On the other hand, LDA+U, method gives good results for the lighter chalcogenides, but it fails to give good results for the heavier cerium monochalcogenides.