Trail making test (TMT) is one of the most extensively used neuropsychological tests. In this study, we examined the equivalence between the iPad version of TMT part A (iTMT-A) and the paper version of TMT part A (pTMT-A), and predicted the cognitive function with various data extracted from repeated TMT-A. Forty-two patients who performed five repeated TMT-A (1st–3rd: iTMT-A, 4th: pTMT-A, 5th: inverse version of iTMT-A) and Mini-Mental State Examination (MMSE) were included. The Kruskal–Wallis one-way analysis of variance revealed no statistical differences between the completion times of iTMT-A and pTMT-A. Factors contributing to the MMSE prediction were selected by stepwise multiple regression analysis and Bland–Altman plots. Then, the prediction abilities of the three models—multiple linear, partial least squares (PLS), and neural network regression—were compared. When using the completion time, the linear regression model with the 1st–5th results exhibited the highest prediction ability. However, when the move time and dwell time were used, the multiple linear and PLS regression models using the 1st and 2nd iTMT-A data exhibited the highest prediction ability. Compared with pTMT-A, iTMT-A extracted a large amount of data with fewer repetitions, and the prediction accuracy of cognitive function was improved.