The present study aimed to assess the changes in the prevalence and determinants of self-reported hypertension among older adults during the COVID-19 pandemic in Bangladesh. This repeated cross-sectional study was conducted on two successive occasions (October 2020 and September 2021), overlapping the first and second waves of the COVID-19 pandemic in Bangladesh. The survey was conducted through telephone interviews among Bangladeshi older adults aged 60 years and above. The prevalence of hypertension was measured by asking a question about whether a doctor or health professional told the participants that they have hypertension or high blood pressure and/or whether they are currently using medication to control it. We also collected information on the socio-economic characteristics of the participants, their cognitive ability, and their COVID-19-related attributes. A total of 2077 older adults with a mean age of 66.7 ± 6.4 years participated in the study. The samples were randomly selected on two successive occasions from a pre-established registry developed by the ARCED Foundation. Thus, the sample in the 2021-survey (round two; n = 1045) was not the same as that in the 2020-survey (round one; n = 1031) but both were drawn from the same population. The findings revealed that the prevalence of hypertension significantly increased across the two periods (43.7% versus 56.3%; p = 0.006). The odds of hypertension were 1.34 times more likely in round two than in the round one cohort (AOR 1.34, 95% CI 1.06-1.70). We also found that having formal schooling, poorer memory or concentration, and having had received COVID-19 information were all associated with an increased risk of hypertension in both rounds (p < 0.05). The findings of the present study suggest providing immediate support to ensure proper screening, control, and treatment of hypertension among older adults in Bangladesh.