The equilibrium crystal structure, band structure, density of states, bulk modulus and its first pressure derivate of CdTe are systemically calculated by first-principles plane-wave pseudo-potential method, and then compared with experimental results. Applying the vibrational Debye-like model, complete sets of isochoric heat capacities can be obtained up to 1000K at pressure or not. With the temperature increasing from 0 to 1000K, a sharp increase in the heat capacity is observed. Moreover, the dependences between cell volume and pressure are also successfully obtained. Our calculated results are in agreement with available results.