应该是Despite his being busy
Despite用作介词时,与 in spite of同义,都表示“尽管”、“虽然”、“不顾”之意
放在句首时,要接成分,成分也就是句子的组成部分,由词或词组充当.
如：
Despite his advanced years,he is learning to drive．
虽然年事已高,他现在在学驾驶汽车.
Despite the drought,we expect a good crop．
尽管天旱,丰收依然在望.