The thermoelectric material is a kind of new functional material, which can convert industrial waste heat and automobile exhaust into the available electric energy by the interaction of carriers. It is widely used in energy, environment, national defense and other fields. For the research of thermoelectric materials, it is the most important to improve the conversion efficiency now. Due to their unique structural properties, the ternary chalcopyrite semiconductors I-III-IV2 (I=Ag, Cu; III=Al, Ga, In; IV=S, Se, Te) display the better thermoelectric performances at high temperature. Many studies show that there are many ways to improve their performances. In order to optimize their thermoelectric efficiencies the structural, elastic and thermoelectric properties of CuGaTe2 and CuInTe2 are studied by employing the density function theory and semi-classical Boltzmann transport theory within the constant time approximation. The electronic band structures are calculated using the Tran-Blaha modified Becke-Johnson potential (MBJ-GGA) and the generalized gradient approximation (GGA). The calculated band gaps with MBJ-GGA of CuGaTe2and CuInTe2 are 0.86 and 0.56 eV, which are more accurate than the calculated values with GGA. The shear modulus, and Young's modulus and sound velocities are determined from the obtained elastic constants. The constant-volume heat capacity is estimated based on the quasi-harmonic Debye model. The calculated temperature dependence of heat capacity agrees very well with the experimental result. Below room temperature, the heat capacity increases quickly with the increasing of temperature. Above room temperature, the heat capacity approaches to the Dulong-Petit limit. In paper, we assume that the lattice thermal conductivities of CuGaTe2 and CuInTe2 are mainly from the phonon scattering. And the phonon scattering is dominated by Umklapp scattering. The calculated lattice thermal conductivities can fit the form kl = A/T-Bin the temperature range of 300-800 K. For CuGaTe2, A = 2869.96 and B = 2.86. The fitting result well approaches to the experimental values and other theoretical results. Based on the calculated band structures with mBJ-GGA potential, the transport properties of CuGaTe2 and CuInTe2 each as a function of chemical potential at various temperatures are investigated. The values of Seebeck coefficient S first increase and then decrease for n-type and p-type doping at low carrier concentrations, which are consistent with the previous results. Electrical conductivity divided by scattering time, i.e. / increases monotonically with chemical potential increasing. The power factor divided by scattering time, i.e. S2/ first increases and then decreases with chemical potential increasing. The magnitude of S2/ increases with temperature increasing. Besides, it is found that the value of S2/ for p-type doping is larger than that for n-type doping. These results show that optimizing the carrier concentration can improve their thermoelectric performances. In order to calculate the electrical conductivity, in this paper we estimate the scattering time from the experiments of Ref.[3]. The CuGaTe2 at 700 K possesses a figure of merit 0.63. These calculated results show that CuGaTe2 and CuInTe2 both are good thermoelectric materials with p-type doping.