Resonance frequency shifts due to radiation fields in the laser-cooled cesium fountain frequency standard, such as the frequency shifts due to microwave spectral impurity, Bloch-Siegert effect, neighboring π transitions, Stark effect, blackbody radiation and Majorana transitions, are investigated, with formulas for evaluating the shifts presented. The magnitudes of the shifts and their uncertainties are evaluated and their effects on the accuracy of the standard are analyzed. In addition, approaches for reducing the shifts and uncertainties are proposed in order to improve the accuracy of the standard. The results obtained here might be of great help for designing the laser-cooled cesium fountain frequency standard and evaluating the accuracy of the standard.