The non-Condon effect plays an important role in the process of electron transfer (ET). Several theoretical models have been proposed to investigate its effect on ET rates. In this paper,we overview a theoretical method for the calculations of the non-Condon ET rate constants proposed by us,and its applications to organic semiconductors. First,full quantum expressions of the non-Condon ET rates are presented with the electronic couplings having exponential,Gaussian and linear dependences in terms of the nuclear coordinates,respectively. The proposed formulas have closed forms in time domain and they thus can be easily applied in multi-mode systems. Then,the driving force dependences of the ET rates involving the non-Condon effect are calculated with the use of full quantum mechanical formulas. It is found that these dependences show very different prop-erties from the Marcus one. As an example of applications,the approaches are used to investigate the non-Condon effect on the mobility of the organic semiconductor dithiophene-tetrathiafulvalene (DT-TTF). The results manifest that the non-Condon ef-fect enhances ET rates compared with the Condon approximation,and static fluctuations of electronic coupling dominate the ET rate in the DT-TTF,which has been confirmed by the molecular dynamics simulation. The non-Condon effect plays an important role in the process of electron transfer (ET). Several theoretical models have been proposed to investigate its effect on ET rates. In this paper, we overview a theoretical method for the calculations of the non-Condon ET rate constants proposed by us, and its applications to organic semiconductors. First, full quantum expressions of the non-Condon ET rates are presented with the electronic couplings having exponential, Gaussian and linear dependences in terms of the nuclear coordinates, respectively. The proposed Formulas have closed forms in time domain and they therefore can be easily applied in multi-mode systems. Then, the driving force dependences of the ET rates involving the non-Condon effect are calculated with the use of full quantum mechanical formulas. It is found that an dependences show very different prop-erties from the Marcus one. As an example of applications, the approach are used to investigate the non-Condon effect on the mobility of the organic semiconductor dithiophene-tetrathiafulvalene (DT-TTF). The results manifest that the non-Condon ef-fect enhances ET rates compared with the Condon approximation, and static fluctuations of electronic coupling dominate the ET rate in the DT-TTF, which has been confirmed by the molecular dynamics simulation.