The number of the subject in English must match the num-ber of the corresponding verb (dog runs but dogs run). Yetin real-time language production and comprehension, speak-ers often mistakenly compute agreement between the verb anda grammatically irrelevant non-subject noun phrase instead.This phenomenon, referred to as agreement attraction, is mod-ulated by a wide range of factors; any complete computationalmodel of grammatical planning and comprehension would beexpected to derive this rich empirical picture. Recent develop-ments in Natural Language Processing have shown that neuralnetworks trained only on word-prediction over large corporaare capable of capturing subject-verb agreement dependen-cies to a significant extent, but with occasional errors. In thispaper, we evaluate the potential of such neural word predic-tion models as a foundation for a cognitive model of real-timegrammatical processing. We use LSTMs, a common sequenceprediction model used to model language, to simulate six ex-periments taken from the agreement attraction literature. TheLSTMs captured the critical human behavior in three out of thesix experiments, indicating that (1) some agreement attractionphenomena can be captured by a generic sequence process-ing model, but (2) capturing the other phenomena may requiremodels with more language-specific mechanisms.