<b><i>Introduction:</i></b> There are several problems with standard in-person neuropsychological assessments, such as habituation, necessity of human resources, and difficulty of in-person assessment under societal conditions during the outbreak of coronavirus disease 2019. Thus, we developed an online cognitive test (the Brain Assessment [BA]). In this study, we investigated the correlation between the results of the BA and those of established neuropsychological tests. <b><i>Participants and Methods:</i></b> Seventy-seven elderly persons (mean 71.3 ± 5.1 years old; range 65–86; male:female = 45:32) were recruited through the internet. Correlations were evaluated between the BA and the following widely used neuropsychological tests: the mini-mental state examination (MMSE), the Raven’s colored progressive matrices (RCPM), the logical memory I and II of the Rivermead Behavioral Memory Test, the word fluency (WF) test, and the Trail-Making TestA/B. <b><i>Results:</i></b> We found moderate correlations between the total cognitive score of the BA and the total score of the MMSE (<i>r</i> = 0.433, <i>p</i> < 0.001), as well as between the total BA score and the total RCPM score (<i>r</i> = 0.582, <i>p</i> < 0.001) and time to complete the RCPM (<i>r</i> = 0.455, <i>p</i> < 0.001). Moderate correlations were also observed between the cognitive score of the memory of words BA subtest and the LM-I (<i>r</i> = 0.518, <i>p</i> < 0.001), the mental rotation subtest and figure drawing (<i>r</i> = 0.404, <i>p</i> < 0.001), the logical reasoning subtest and total RCPM score (<i>r</i> = 0.491, <i>p</i> < 0.001), and the memory of numbers and words subtests and WF (memory of numbers and total WF: <i>r</i> = 0.456, <i>p</i> < 0.001; memory of words and total WF: <i>r</i> = 0.571, <i>p</i> < 0.001). <b><i>Discussion:</i></b> We found that the BA showed moderate correlations between established neuropsychological tests for intellect, memory, visuospatial function, and frontal function. The MMSE and the RCPM reflect Spearman’s s-factor and g-factor, respectively, and thus the BA also covered both factors. <b><i>Conclusion:</i></b> The BA is a useful tool for assessing the cognitive function of generally healthy elderly persons.