Previous research has indicated that meaningful background speech affects individuals reading comprehension performance differently and that this difference is related to working memory capacity. But what mechanism in working memory that is involved is not well understood. The present study’s main purpose was to investigate if individual differences in susceptibility to effects of speech on reading comprehension are moderated by working memory capacity as measured by the number updating task and two different mechanisms within this construct; delayed suppression (i.e. the inhibition of information that once was task-relevant but no longer is) and immediate suppression (i.e. the inhibition of processed but irrelevant information, while withholding attention focused on the to-be-recalled task-relevant items). Forty participants performed a number updating task and a reading comprehension task in silence and with meaningful background speech. The results indicated that the immediate suppression mechanism moderates the effects of background speech on reading comprehension. Those who can’t handle the interference from the background speech let the task-irrelevant information interfere with the ongoing cognitive task and therefore are more likely to be distracted by the background speech while reading a text.