Previous neuroimaging studies have reported dual-task interference (DTi) and deterioration of task performance in a cognitive-motor dual task (DT) compared to that in a single task (ST). Greater frontoparietal activity is a neural signature of DTi; nonetheless, the underlying mechanism of cortical network in DTi still remains unclear. This study aimed to investigate the regional brain activity and neural network changes during DTi induced by highly demanding cognitive-motor DT. Thirty-four right-handed healthy young adults performed the spiral-drawing task. They underwent a paced auditory serial addition test (PASAT) simultaneously or independently while their cortical activity was measured using functional near-infrared spectroscopy. Motor performance was determined using the balanced integration score (BIS), a balanced index of drawing speed and precision. The cognitive task of the PASAT was administered with two difficulty levels defined by 1 s (PASAT-1 s) and 2 s (PASAT-2 s) intervals, allowing for the serial addition of numbers. Cognitive performance was determined using the percentage of correct responses. These motor and cognitive performances were significantly reduced during DT, which combined a drawing and a cognitive task at either difficulty level, compared to those in the corresponding ST conditions. The DT conditions were also characterized by significantly increased activity in the right dorsolateral prefrontal cortex (DLPFC) compared to that in the ST conditions. Multivariate Granger causality (GC) analysis of cortical activity in the selected frontoparietal regions of interest further revealed selective top-down causal connectivity from the right DLPFC to the right inferior parietal cortex during DTs. Furthermore, changes in the frontoparietal GC connectivity strength between the PASAT-2 s DT and ST conditions significantly correlated negatively with changes in the percentage of correct responses. Therefore, DTi can occur even in cognitively proficient young adults, and the right DLPFC and frontoparietal network being crucial neural mechanisms underlying DTi. These findings provide new insights into DTi and its underlying neural mechanisms and have implications for the clinical utility of cognitive-motor DTs applied to clinical populations with cognitive decline, such as those with psychiatric and brain disorders.