The structural, electronic, elastic and optical properties of CdxZn1-xTe ternary mixed crystals are investigated by the first-principles plane-wave pseudopotential method within the LDA approximations. Basic physical properties, such as lattice constant, bulk modulus, second-order elastic constants (C-ij) and the electronic band structures, are calculated. We also predict the shear modulus, Young's modulus and Poisson's ratio. Moreover, we have calculated the optical properties (dielectric functions, refractive index, extinction coefficient and energy loss function) of these ternary mixed crystals. Our results agree well with the available data in the literature.