The process model of emotion regulation suggests that cognitive reappraisal and expressive suppression engage at different time points in the regulation process. Although multiple brain regions and networks have been identified for each strategy, no articles have explored changes in network characteristics or network connectivity over time. The present study examined (a) the whole-brain network and six other resting-state networks, (b) their modularity and global efficiency, which is an index of the efficiency of information exchange across the network, (c) the degree and betweenness centrality for 160 brain regions to identify the hub nodes with the most control over the entire network, and (d) the intra-network and inter-network functional connectivity (FC). Such investigations were performed using a traditional large-scale FC analysis and a relatively recent sliding window correlation analysis. The results showed that the right inferior orbitofrontal cortex was the hub region of the whole-brain network for both strategies. The present findings of temporally altering functional activity of the networks revealed that the default mode network (DMN) activated at the early stage of reappraisal, followed by the task-positive networks (cingulo-opercular network and fronto-parietal network), emotion-processing networks (the cerebellar network and DMN), and sensorimotor network (SMN) that activated at the early stage of suppression, followed by the greater recruitment of task-positive networks and their functional connection with the emotional response-related networks (SMN and occipital network). This is the first study that provides neuroimaging evidence supporting the process model of emotion regulation by revealing the temporally varying network efficiency and intra- and inter-network functional connections of reappraisal and suppression.