Within the t-J model and the microscopic theory of the cuprate superconductors, the temperature dependence of the normal state thermopower S(T) of cuprate superconductors is studied in the whole doping range. It is shown that by regard the electron dispersion as a mixture of the charge-carrier dispersion and the bare electron dispersion, the experimental results of the thermopower in cuprate superconductors at the normal state are qualitatively reproduced. In particular, the partial correlation effect is thought to be essential to the nonlinear behavior of S(T) by enhance the asymmetry of the spectral conductivity near the electron Fermi surface. The positive or negative value of the thermopower at low temperature is decided by the relative position of the peak in the spectral conductivity.