Introduction Repetitive transcranial magnetic stimulation (rTMS) is a noninvasive tool for modulating cortical activity. Objectives In this pilot study, we evaluated the effects of high frequency rTMS applied over the right inferior frontal gyrus (IFG) on cognitive functions in patients with amnestic mild cognitive impairment (MCI) or incipient dementia due to Alzheimer’s disease (AD). Methods Ten patients (6 men; 4 women, mean age 72 ± 8 years; MMSE 23 ± 3.56) were enrolled in a randomized, placebo-controlled study with a crossover design. All participants received 2 sessions of 10 Hz rTMS over the non-dominant right hemisphere in random order: IFG (active stimulation site) and vertex (control stimulation site). Intensities were adjusted to 90% of resting motor threshold. A total of 2250 pulses were applied in a session. The Trail Making Test (TMT), the Stroop test, and the complex visual scene encoding task (CVSET) were administered before and immediately after each session. The Wilcoxon paired test was used for data analysis. Results Stimulation applied over the IFG induced improvement in the TMT parts A (p = 0.037) and B (p = 0.049). No significant changes were found in the Stroop test or the CVSET after the IFG stimulation. We observed no significant cognitive aftereffects of rTMS applied over the vertex. Conclusions High frequency rTMS of the right IFG induced significant improvement of attention and psychomotor speed in patients with MCI/mild dementia due to AD. This pilot study is part of a more complex protocol and ongoing research.