Given the widespread use and relapse of methamphetamine (METH), it has caused serious public health burdens globally. However, the neurobiological basis of METH addiction remains poorly understood. Therefore, this study aimed to use magnetic resonance imaging (MRI) to investigate changes in brain networks and their connection to impulsivity and drug craving in abstinent individuals with METH use disorder (MUDs). A total of 110 MUDs and 55 age- and gender-matched healthy controls (HCs) underwent resting-state functional MRI and T1-weighted imaging scans, and completed impulsivity and cue-induced craving measurements. We applied independent component analysis to construct functional brain networks and multivariate analysis of covariance to investigate group differences in network connectivity. Mediation analyses were conducted to explore the relationships among brain-network functional connectivity (FC), impulsivity, and drug craving in the patients. MUDs showed increased connectivity in the salience network (SN) and decreased connectivity in the default mode network compared to HCs. Impulsivity was positively correlated with FC within the SN and played a completely mediating role between METH craving and FC within the SN in MUDs. These findings suggest alterations in functional brain networks underlying METH dependence, with SN potentially acting as a core neural substrate for impulse control disorders.