Eph. 1:5 - Paul teaches that God "predestined" us in love to be His sons through Jesus Christ. "Predestination" means that God knows what we will do before we do it (it does not mean that God determines what we do; otherwise, we would have no free will). Predestination is taken from the Greek word "prooridzo" which means to know or declare in advance by God's foreknowledge. See, for example, 1Peter 1:2 where Peter writes about the "elect according to the foreknowledge of God." The terms "predestination" and "the elect" alway refer to God's knowledge (not human knowledge) because God is outside of time (and humans cannot predict the future). There are two tyes of "predestination," to grace and to glory. In this verse, paul is teaching about predestination to grace, which means becoming a Christian.
1Pet.1:1-2 - teaches about being destined by God for obedience to Christ. This is another example of predestination to grace. But there is also predestination to glory.
Rom. 8:29-30 - Paul also wries that we are predestined to be conformed to the image of His Son. Now Paul is writing about predestination to glory, which means not only becoming a faithful Christian during our lives, but perservering to the end by conforming our will to Christ's will.
1Cor. 15:49 - Paul writes that we are conformed in His image at the ressurection, when we shall bear the image of man in heaven. These are the people who are predestined to gory.
Rev. 3:5 - Jesus warns that He can blot out the names that are in the book of life. This refers to those currently, not ultimately, justified (those who are predestined to grace not to glory).
Eph 1:5; 1Peter 1:2; Rom. 8:29-30; 1 Cor. 15:49 - therefore, predestination is either to grace (which we could lose) or to glory (which we cannot lose). As alluded to above, some non-Catholics confuse the definition "predestination" (which means God knows what we will do before we do it) and "predetermination" (the erroneous belief that god determines what we will do). But God does not author evil. We choose evil by our free will.
Ezek 18:23-24, 32 - God takes no pleasure in the death of the wicked. Our death is our free will, failing to respond to His grace. God does not predetermine certain people to hell. God does not also predetermine certain people to heaven. We all, as God's children, have been given the grace needed to be saved, but we can decide to reject God's grace.
2 Peter 3:9 - God is forebearing toward you, not wishing that any should perish, but that all should reach repentence. God's wills all to be saved., but our salvation depends on our willingness to repent and receive God's grace.
Matt. 18:14 - Jesus says it is not the will of the father that any should perish, but he has given us free will to choose.
1Tim. 2:4, 2Pet. 3:9, James 1:13 - 14, 1 Cor. 10:13.
All these verses speak of predestination.