WASHINGTON—Donald Trump, fresh from his latest series of primary wins, will deliver a rare policy speech Wednesday aimed at calming some Republicans’ fears about his ability to deal with global crises.

Mr. Trump’s speech, to be delivered in Washington, D.C., is part of an effort to present the GOP front-runner as a leader ready to become commander-in-chief, following months of raucous rallies and incendiary statements about his competitors, ethnic groups and sometimes other countries.

...