Structural, elastic, electronic and optical properties of the Pt3Zr intermetallic compound are investigated using first principles calculations based on the density functional theory (DFT) within the generalized gradient approximation (GGA) and the local density approximation (LDA). The Pt3Zr compound is predicted to be of cubic L12 and hexagonal D024 structures. The calculated equilibrium ground-state properties (lattice parameters a and c, bulk modulus B and its pressure derivative B′, formation enthalpy ΔH) of the Pt3Zr compound, for both cubic and hexagonal phases, show good agreement with the experimental results and other theoretical data. Elastic constants (C
11, C
12, C
13, C
33, C
44, and C
55) are calculated. The predicted elastic properties such as Young’s modulus E and shear modulus G
H, Poisson ratio ν, anisotropic ratio A, Kleinman parameter ξ, Cauchy pressure (C
12−C
44), ratios B/C
44 and B/G, and Vickers hardness H
v indicate the stiffness, hardness and ductility of the compound. Thermal characteristic parameters such as Debye temperature θ
D and melting temperature T
m are computed. Electronic properties such as density of states (DOS) and electronic specific heat γ are also reported. The calculated results reveal that the Fermi level is on the psedogap for the D024 structure and on the antibonding side for the L12 structure. The optical property functions (real part ε
1(ω) and imaginary part ε
2(ω) of dielectric function), optical conductivity σ(ω), refraction index n(ω), reflectivity R(ω), absorption α(ω) and extinction coefficients k(ω) and loss function L(ω)) are also investigated for the first time for Pt3Zr in a large gamme of energy from 0 to 70 eV.