Motor imagery (MI) based brain-computer interface (BCI) has been extensively studied and advanced in several fields of applied brain science. This study investigates a neurofeedback training protocol for left- and right-hand grasp MI-BCI systems. An obstacle within MI-BCI is the inability of participants to perform the BCI task, commonly referred to as BCI illiteracy. Low performance amongst these users is common as well. To improve the performance of BCI, various training protocols have been investigated by other research groups. The problem with these protocols is that they are designed with a balanced dataset. Similarly, regarding the biases seen towards hand dominance for motor execution tasks, participants have also shown a performance bias in MI tasks. A trial-adjusted neurofeedback protocol is proposed to address this MI bias in participants. The number of trials in each condition is adjusted for the proposed neurofeedback by MI bias. Trials are adjusted to increase the number of times participants can perform their weak MI task. This study aims to investigate the effects the trial-adjusted neurofeedback had on participants' cognitive and classification performance in the MI-BCI. Band power analysis and classification evaluations are investigated to identify the effects of the proposed neurofeedback. Both the band power analysis and classification performance results show a difference in effect between control-balanced neurofeedback and the proposed trial-adjusted neurofeedback. The trial-adjusted neurofeedback positively affects participants' cognitive performance and classification ability in MI-BCI. This study demonstrates the positive effects of neurofeedback when addressing the bias in MI performance.