In clinical trials, various randomization strategies have been developed to allocate subjects to different interventions or treatment arms. The preferred strategy is one that balances the distribution of covariates across the treatment arms and assigns more subjects to the treatments associated with better outcomes. Sequential multiple assignment randomized trial (SMART) designs involve an initial stage in which participants are randomized to a set of intervention options, followed by subsequent stages in which some or all of the individuals are re-randomized to the intervention options available at that stage. For SMART designs, the intervention for each subject can be optimized individually using a Q-learning-based optimization algorithm. However, such response-adaptive or Q-learning-based randomization strategies lead to covariate imbalance that can result in biased inference when the imbalanced covariates are associated with the outcome of interest, particularly with small to moderate sample sizes. To combine the advantages of Q-learning-decision-consistent strategies and response-adaptive designs while controlling for covariate balance, we propose a Bayesian response-adaptive, covariate-balanced and Q-learning-decision-consistent randomization method (RCQ) for SMART designs. Simulation studies to illustrate the performance of the proposed method show that the RCQ randomization method assigned the lowest percentage of subjects to the inferior intervention arms and the highest percentage of subjects to optimal Q-learning-decision-consistent strategies that maximize the long-term outcome for the individual while exhibiting well-controlled covariate balance. The alternative randomization strategies showed pronounced covariate imbalance or assigned higher percentages of subjects to inferior interventions or were not consistent with the Q-learning-based optimal decision strategy.