This paper reports the results of using multiple-ring microchannels for enhancing liquid-liquid extraction performance. The effects of geometrical parameters including ring and distance characteristics on the extraction efficiency were studied. The mass transfer performance was analyzed using Water+Alizarin Red S+1-octanol system. By change in geometrical parameters, the extraction efficiency of multiple-ring microchannels improved up to 62.9% compared with that of the plain one. The performance ratio is defined based on two contrary effects of friction factor and extraction efficiency for evaluating the extraction performance. A performance ratio of 1.5 was achieved that confirmed the advantage of using this type of microfluidic extraction system. Artificial neural network and adaptive neurofuzzy inference system were utilized to evaluate the performance ratio of the multiple-ring microchannels. The mean relative error values of the testing data were 0.397% and 0.888% for the neural network and the neuro-fuzzy system, respectively. The estimation accuracy for both models is appropriate, but the precision of the neural network id higher than that of the neuro-fuzzy system. The genetic algorithm approach was employed to develop a new empirical correlation for predicting the performance ratio with a mean relative error of 1.558%.