If you are running a Verizon Galaxy S4 that is on software VRUAME7, there is now a way to root your phone, just follow the steps to have it done.
Source: http://www.phonearena.com/news/Have-no-fear-newest-Root-method-for-the-Verizon-Samsung-Galaxy-S4-is-here_id46031
Source: http://www.phonearena.com/news/Have-no-fear-newest-Root-method-for-the-Verizon-Samsung-Galaxy-S4-is-here_id46031