The aim of this study is to simulate the transport of degraded nitrate by nano-Fe/Cu particles in the length of a packed sand column. A meta-modeling approach based on the adaptive neuro-fuzzy inference system (ANFIS) method and a finite volume modeling of the 1D advection-dispersion-reaction equation (ADRE) have been used for simulation of this system. A mixed order kinetic reaction model (Monod-type kinetics) has been used for sink/source term in ADRE. In the ANFIS modeling, three scenarios have been designed to determine the model's optimum set of input-output variables. The comparison results show that in spite of capability of the ANFIS as a powerful tool for data-oriented modeling, the physical-based model for advection-dispersion-reaction phenomena is more efficient in nitrate transport simulation in the presence of nano-Fe/Cu particles.