Electrical current can effectively improve the plasticity of metallic materials. The tensile deformation behavior of Al alloys under the pulsed electrical current assisted quasi-static unidirectional tension (EAT) has been investigated. Materials under the EAT exhibits periodic electro-softening and strain-hardening behaviors, i.e., a ratchet shape mechanical response. However, establishing a constitutive model to accurately predict the ratchet shape mechanical behavior, especially during the EAT interval, and accurately predicting the strain-hardening behavior of materials are critical issues that need to be solved urgently. In this study, based on the Taylor polycrystalline model, thermal activation theory and dislocation density evolution theory, a two-parameter dislocation density electroplasticity constitutive model with forward and reverse dislocation density evolution was developed to describe the periodic coupling effect of the electro-thermal-mechanical fields during EAT. The tensile deformation behaviors of AA 6061-T6 and AA 7075-T6 under the effect of a pulsed electrical current were quantitatively predicted using the proposed constitutive model. The results show that the correlation coefficient between the predicted and experimental results of the constitutive model can reach 0.84–0.99, implying that the proposed constitutive model can accurately predict the complex electroplasticity behavior of Al alloys during EAT.