这两个要看怎么用了!一般情况下是be about to do sth.意思是将要做某事.例如 He is about to study.(他要去学习了).
about doing sth一种是因为about是一个介词,介词后面要跟名词,所以把动词该成动名词加上ing,另一种是固定句型,例如How zbout doing sth.或者What about doing sth.意思是干什么怎么样.