There has been increasing condemnation of Mr Trump's immigration ban for seven mainly Muslim countries.
On Saturday the 9th US Circuit Court of Appeals upheld a restraining order on the original travel ban.
The White House directive had suspended the nation's refugee programme and barred all entries from seven Muslim-majority countries.
It had received widespread criticism but Graham, one of America's most high profile Christians, posted on Facebook that he had "something to say about this issue".
He said his view was informed because his charity, Samaritan's Purse, was working in most of the countries on the banned list.
Many Christian leaders slammed the ban as un-Christian, saying that Jesus told us to welcome the stranger.
"But that doesn't mean we don't need to make the borders of our own country secure," warned Graham on Facebook on Saturday.
"We shouldn't be naïve. Just because we give medical care to ISIS fighters doesn't mean I would want to allow any one of them to immigrate to the United States. That would be crazy.
"Taking time to vet who we're allowing to enter America isn't too much to ask-we need to know who they are. God does tell us to help the stranger and those in need; but God doesn't tell us to expose our cities, homes, and lives to hostile people."
Graham said there was a "fundamental incompatibility" between the way Muslims live and the American constitution.
Meanwhile more than 500 evangelical leaders and pastors, including Stuart and Jill Briscoe, have signed a letter against the travel ban.
Every state is represented in the letter which says: "As Christians, we have a historic call expressed over two thousand years, to serve the suffering. We cannot abandon this call now."
Donald Trump said he was considering signing a "brand new order".