Background: The purpose of the present study was to compare the influence of an acute bout of high-intensity functional training (HIFT) with an acute bout of moderate-intensity continuous training (MICT) on measures of cognitive function. Methods: Sixty-nine young adults (Mean ± SD: age = 21.01 ± 2.79 yrs; body mass = 69.65 ± 6.62 kg; height = 1.74 ± 0.05 m; Body Mass Index = 22.8 ± 1.41) gave informed consent and were randomly divided into three groups. The HIFT group, with 27 participants, performed a high-intensity (>85% Max. HR) circuit of functional exercises for 30 min. The MICT group, with 28 participants, performed moderate-intensity (70–80% Max. HR) continuous training on a cyclo-ergometer. The control group did not perform any activity. The Stroop Test, Word Recall and N-Back Test were completed to assess during the familiarization period, immediately before and immediately after the training’s bouts. Results: The repeated measures ANOVA did not show significant mean differences for any group. However, the T-Test for the paired samples demonstrated very significant differences in the Stroop Test, in terms of fastest response time (FRT; mean difference (MD) = −1.14, p < 0.01, d = 0.9), mean response time (MRT; MD = −2.16, p < 0.01, d = 0.66) and the number of correct answers (NCA; MD = 1.08, p < 0.05, d = 0.5) in the HIFT group and in the MICT group (FRT; MD = −1.79, p < 0.01, d = 0.9), (MRT; MD = −3.07, p < 0.01, d = 0.9) (NCA; MD = 1.54, p < 0.05, d = 0.5). Conclusions: There were no differences in the control group. HIFT and MICT may elicit specific influences on cognitive function, mainly in executive function and selective attention.