Using the effective mass approximation and the iterative procedure, we study the optical rectification (OR) coefficient of a spherical quantum dot (QD) system with like-screened Kratzer potential (LSKP), taking into account the influence of the confinement potential depth, quantum size and external environment. Our results show that the magnitude of the OR coefficient is strongly dependent on the magnitude of the tunable factor, whose peak value will be red-shifted or blue-shifted. Interestingly, the limiting potential depth and temperature have opposite effects on the OR coefficient in terms of peak location and size. Therefore, it is necessary to pay more attention to the influence of internal and external parameters on nonlinear optical effects, and apply the theory to practical experiments and the manufacture of optoelectronic devices.