Randomization is a distinguishing feature of clinical trials for unbiased assessment of treatment efficacy. With a growing demand for more flexible and efficient randomization schemes and motivated by the idea of adaptive design, in this article we propose the network and covariate adjusted response‐adaptive (NCARA) design that can concurrently manage three challenges: (1) maximizing benefits of a trial by assigning more patients to the superior treatment group randomly; (2) balancing social network ties across treatment arms to eliminate potential network interference; and (3) ensuring balance of important covariates, such as age, gender, and other potential confounders. We conduct simulation with different network structures and a variety of parameter settings. It is observed that the NCARA design outperforms four alternative randomization designs in solving the above‐mentioned problems and has comparable power and type I error for detecting true difference between treatment groups. In addition, we conduct real data analysis to implement the new design in two clinical trials. Compared to equal randomization (the original design utilized in the trials), the NCARA design slightly increases power, largely increases the percentage of patients assigned to the better‐performing group, and significantly improves network and covariate balances. It is also noted that the advantages of the NCARA design are augmented when the sample size is small and the level of network interference is high. In summary, the proposed NCARA design assists researchers in conducting clinical trials with high‐quality and high‐efficiency.