Brain-computer interfaces (BCIs) allow control of various applications or external devices solely by brain activity, e.g., measured by electroencephalography during motor imagery. Many users are unable to modulate their brain activity sufficiently in order to control a BCI. Most of the studies have been focusing on improving the accuracy of BCI control through advances in signal processing and BCI protocol modification. However, some research suggests that motor skills and physiological factors may affect BCI performance as well. Previous studies have indicated that there is differential lateralization of hand movements' neural representation in right- and left-handed individuals. However, the effects of handedness on sensorimotor rhythm (SMR) distribution and BCI control have not been investigated in detail yet. Our study aims to fill this gap, by comparing the SMR patterns during motor imagery and real-feedback BCI control in right- (N = 20) and left-handers (N = 20). The results of our study show that the lateralization of SMR during a motor imagery task differs according to handedness. Left-handers present lower accuracy during BCI performance (single session) and weaker SMR suppression in the alpha band (8-13 Hz) during mental simulation of left-hand movements. Consequently, to improve BCI control, the user's training should take into account individual differences in hand dominance.