High blood pressure is associated with an elevated risk of dementia. However, much less is known about how high blood pressure is related to cognitive deficits in domains including episodic memory, semantic verbal fluency, fluid reasoning, and numerical ability. By analyzing data from 337 participants (57.39% female) with a history of clinical high blood pressure diagnosis with a mean age of 48.78 ± 17.06 years and 26,707 healthy controls (58.75% female) with a mean age of 45.30 ± 15.92 years using a predictive normative modeling approach and one-sample t-tests, the current study found that people with high blood pressure have impaired immediate (t(259) = −4.71, p < 0.01, Cohen’s d = −0.08, 95% C.I. [−0.11, −0.05]) and delayed word recall (t(259) = −7.21, p < 0.01, Cohen’s d = −0.11, 95% C.I. [−0.15, −0.08]) performance. Moreover, people with high blood pressure also exhibited impaired performance in the animal naming task (t(259) = −6.61, p < 0.0001, Cohen’s d = −0.11, 95% C.I. [−0.15, −0.08]), and number series (t(259) = −4.76, p < 0.01, Cohen’s d = −0.08, 95% C.I. [−0.11, −0.05]) and numeracy tasks (t(259) = −4.16, p < 0.01, Cohen’s d = −0.06, 95% C.I. [−0.09, −0.03]) after controlling for demographic characteristics. Clinicians and health professionals should consider including these tasks as part of the neuropsychological assessment for people with high blood pressure, to detect their cognitive deficits. Moreover, they should also come up with ways to improve cognitive performance in people with high blood pressure.