Fighting in Vietnam was an experience that would haunt him for the rest of his life.

haunt 是动词，本意是"（鬼魂）出没、萦绕"，引申为"（记忆或情感）长期困扰、挥之不去"。这里用 haunt 的动词原形表示"会持续不断地困扰"这种未来状态。