This computational study focused on the optical properties of zinc antimonide ZnSb. It relates to the complex dielectric function ε (ω), the refractive index n (ω), the extinction function k (ω), the optical conductivity σ (ω), the reflectivity R(ω), the absorption coefficient α (ω) and the energy loss spectrum L(ω). These properties are calculated and discussed for a growing energy of the incident electromagnetic radiation ranging from 0 to 14 eV, comprising infrared, visible and ultraviolet regions. All these properties are obtained using the Full Potential Linearized Augmented Plane Wave (FP-LAPW), by solving Kohn-Sham equations. This method based on Density Functional Theory (DFT), implemented in Wien2k simulation package. This compound is already used in photo-optical applications, it is for this reason that we interested in the calculation of its optical properties according to the energy of the incident photons, in order to open up for it other use ways. Since the zinc antimonide ZnSb is a semiconductor, its optical properties are investigated using Generalized Gradient Approximation plus modified Becke–Johnson as the exchange correlation (GGA-mBJ). Our calculations are performed by considering only the interband transition of electrons between the occupied states in valence band and unoccupied conduction band states along high symmetry points in Brillouin zone. In addition, the relations of the optical properties to these transitions are discussed in detail. We have also verified the Penn’s model by showing the inverse relationship between the static real part of dielectric function ε1(0) and the optical band gap Eg. The results obtained are compared with other results existing in the literature.