We know from the literature that high cognitive load can impede performance and educational outcomes. Previous measures of cognitive load have largely relied on subjective scales but few have explored more objective measures. This paper aims to address this issue by examining the validity of electroencephalography (or EEG) as an objective measure of cognitive load in the context of educational video. EEG is an online brain measure of the electrical activity that a population of neurons elicits when they are activated. Theta power is a brain oscillation ranging from 4 to 7 Hz that has been linked to cognitive and memory performance. We manipulated the linguistic complexity of three texts delivered by a speaker on video to induce a simple, a moderate and a complex level of cognitive load amongst a sample of students pursuing postgraduate studies through the medium of English as a second language (n = 35). We specifically measured intrinsic cognitive load via a subjective scale, a recall test, and theta power as an objective measure (average cognitive load). Our results show that the subjective scale was significantly different across the three levels of linguistic complexity. However, theta power and recall were only significantly different between the two most distinct levels of linguistic complexity. Although, this finding suggests theta power may not be as sensitive for average cognitive load as the subjective scale for intrinsic cognitive load, a correlation analysis shows that theta power was correlated with self-reported cognitive load. However, it may need more power compared to the subjective scale. These findings suggest that theta power may be developed into a valid objective measure of average cognitive load although its true potential lies in the possibility to measure online fluctuations in cognitive load or instantaneous cognitive load.