If by "no political background" you mean never having held an elected position before running for president, then yes, we've had a few presidents like that. Dwight Eisenhower had been the Supreme Allied Commander during the Second World War, the Governor of the American occupied zone in Germany (for a few months), Chief of Staff of the United States Army, and then president of Columbia University. But he was never an elected official before running for president.

Likewise, Ulysses S. Grant held no elected position before running for president. He went straight from Commanding General of the United States Army to President.

And Zachary Taylor, major general of the United States Army and "hero" of the Mexican-American war, became president without having held another elected office.

By this strict definition, you could even include William Taft, as he was appointed to several (judge, governor of the Philippines, Secretary of War, to name a few) political positions before running for president, but here the definition fails as he was clearly very politically active before becoming president. Likewise, Herbert Hoover was Secretary of Commerce before running for president, without holding an elected position prior to his run as president.

As you can see, popular military leaders without any experience as an elected official have become President of the United States in the past. Of course, you could readily argue that they knew well the politics of the military and so could claim a background in politics of a sort.

But nobody like Trump--that is, a civilian who never held a political office of any kind--has ever become president.