Abstract W3 is one of the most outstanding regions of high-mass star formation in the outer solar circle, and includes two active star-forming clouds: W3 Main and W3(OH). Based on a new analysis of the ${^{12}\text{CO}(J = 2-1)}$ data obtained at $38^{\prime \prime }$ resolution, we have found three clouds that have molecular masses from 2000 to $8000\, {M_\odot }$ at velocities $-50\:\rm{km\: s^{-1}}$, $-43\:\rm{km\:s^{-1}}$, and $-39\:\rm{km\:s^{-1}}$. The $-43\:\rm{km\:s^{-1}}$ cloud is the most massive one, overlapping with the $-39\:\rm{km\:s^{-1}}$ cloud and the $-50\:\rm{km\:s^{-1}}$ cloud toward W3 Main and W3(OH), respectively. In W3 Main and W3(OH), we have found typical signatures of a cloud–cloud collision, i.e., the complementary distribution with/without a displacement between the two clouds and/or a V-shape in the position–velocity diagram. We frame a hypothesis that a cloud–cloud collision triggered the high-mass star formation in each region. The collision in W3 Main involves the $-39\:\rm{km\:s^{-1}}$ cloud and the $-43\:\rm{km\:s^{-1}}$ cloud. The collision likely produced a cavity in the $-43\:\rm{km\:s^{-1}}$ cloud that has a size similar to the $-39\:\rm{km\:s^{-1}}$ cloud and triggered the formation of young high-mass stars in IC 1795 $2\:$Myr ago. We suggest that the $-39\:\rm{km\:s^{-1}}$ cloud is still triggering the high-mass objects younger than $1\:$Myr currently embedded in W3 Main. On the other hand, another collision between the $-50\:\rm{km\:s^{-1}}$ cloud and the $-43\:\rm{km\:s^{-1}}$ cloud likely formed the heavily embedded objects in W3(OH) within $\sim\! 0.5\:$Myr ago. The present results favour an idea that cloud–cloud collisions are common phenomena not only in the inner solar circle but also in the outer solar circle, where the number of reported cloud–cloud collisions is yet limited (Fukui et al. 2021, PASJ, 73, S1).