He was trying to think of everything he would have needed.
manamiさんの言うように、He was trying to think of everything he would need. と言うと「彼は必要なもの全てを考えようとした」となります。「必要だったもの」にするなら、he would have needed と言うと良いでしょう。
例:
He was trying to think of everything he would have needed for the camping trip.
「彼はキャンプ旅行に必要だったものを考えようとした」
ご参考まで!