In this population-based propensity score matched (PSM) cohort study, we aimed to investigate the risk of developing dementia with the use of acid suppressants, including proton pump inhibitors (PPIs) and histamine-2 receptor antagonists (H2 antagonists). Cohorts of PPI users (n = 2,778), H2 antagonist users (n = 6,165), and non-users (n = 86,238) were selected from a dataset covering the years 2000 to 2010 in Taiwan’s National Health Insurance Research Database. Patients in the three groups were PSM at a ratio of 1:1 within each comparison cohort (CC). Three CCs were created: (1) PPI users compared to non-users (CC1, n = 2,583 pairs); (2) H2 antagonist users compared to non-users (CC2, n = 5,955 pairs); and (3) PPI users compared to H2 antagonist users (CC3, n = 2,765 pairs). A multivariable robust Cox proportional hazard model was used to estimate the adjusted hazard ratio (aHR) and the 95% confidence interval (CI) for the risk of developing dementia. The multivariable analysis results show that the aHR of developing dementia during the follow-up period was 0.72 (CC1: 95% CI = 0.51–1.03, P = 0.07) for PPI users and 0.95 (CC2: 95% CI = 0.74–1.22, P = 0.69) for H2 antagonist users, when compared to non-users. Between the patients using acid suppressants, there was no difference between PPI and H2 antagonist users in the risk of developing dementia (CC3: aHR = 0.82, 95% CI = 0.58–1.17, P = 0.28). In conclusion, no association was observed between the use of acid suppressants and the risk of developing dementia in any of the three CCs. Further, randomized controlled trials are warranted to confirm this relationship.