From a psycholinguistic perspective of view, there are many cognitive differences that matter to individuals' second-language acquisition (SLA). Although many computer-assisted tools have been developed to capture and narrow the differences among learners, the use of these strategies may be highly risky because changing the environments or the participants may lead to failure. In this paper, we propose an artificial neural network (ANN)-based computational model to simulate the environment to which students are exposed. The ANN computational model equips English teachers with the ability to quickly find the predicting factors to learners' overall English competences and also provides teachers with the ability to find abnormal students, based on reviewing their individualized ANN trajectories. Finally, by observing the compound effects of cognitive factors using the same evaluation scale, new hypotheses about the mutual relationships among the phonological awareness, phonological short-term memory, and long-term memory abilities of their students can be generated. Our experimental ANNs suggested three detailed corresponding conclusions for the participants' English teachers. These results provide teachers with guidance in designing and applying cognitive ability-related intervention strategies in their L2 pedagogical activities.