#1037 rejects double-predestination, not predestination as a whole. The Catechism also mentions God’s plan of predestination in #600.
As I said, predestination is a dogma of the faith and must be held by the faithful and there is a very interesting body of theology behind it, way richer than what the Catechism tells us in passing.
This is the teaching (as stated in Ott):
GOD, BY HIS ETERNAL RESOLVE OF WILL, HAS PREDETERMINED CERTAIN MEN TO ETERNAL BLESSEDNESS (De fide)
(The “de fide” tells us this is a binding teaching. Catholics are not free to reject it).
This doctrine is proposed by the Ordinary and General Teaching of the Church as a truth of Revelation. The doctrinal definitions of the Council of Trent presuppose it . . . The reality of Predestination is clearly attested to in Rom 8:29 et seq: . . . cf. Mt 25:34, Jn 10:27 et seq., Acts 13:48, Eph 1:4 et seq. . . . Predestination is a part of the Eternal Divine Plan of Providence.
And the shocker that alarms many Catholics, but is also binding Church teaching is this:
GOD, BY AN ETERNAL RESOLVE OF HIS WILL, PREDESTINES CERTAIN MEN, ON ACCOUNT OF THEIR FORESEEN SINS, TO ETERNAL REJECTION (De fide)
The reality of Reprobation is not formally defined, but it is the general teaching of the Church.
This, however, is NOT the same as Calvinistic double-predestination, which does NOT account for foreseen demerits, but is explained nicely with the Molinist school of thought.
Ultimately, it is just these two that we need to accept, although a study of the Thomist and Molinist views is very enlightening and interesting. However, predestination is one of the most difficult theological topics, which is why other than the basics of the teachings given above, the Church has not defined exactly how this happens.