Yes. There is free will and predestination. People have free will, and God has predestined a plan for all of mankind.
Here are two scriptures that show man has free will or the ability to choose the direction he takes in his life. In Matt 7:21 Jesus says, "Not everyone who says to Me, ‘Lord, Lord,’ will enter the kingdom of heaven, but he who does the will of My Father who is in heaven will enter.” In Matt 12:50 Jesus says, “For whoever does the will of My Father who is in heaven, he is My brother and sister and mother.” These scriptures imply that humans have the choice to do or not do the will of the heavenly Father. Individuals are not programmed to do God’s will. Just as Adam chose to disobey God, each person has the ability to choose to obey or disobey. The scriptures are full of examples of free will, where God did not force an individual to make a choice. Look at the story of Job – he was tempted to swear against God for all that had happened to him, but he made the choice by himself to remain faithful to God. We could point to many others such as Lucifer, Abraham, David, Judas, and Jesus as examples of ones who made their own choice to either follow or not follow God’s will.
As for predestination, the scriptures clearly speak of God predestinating a group of people to be his followers. He does not however predestinate the choices of an individual. Let’s look at Eph 1:4-5: (NASB): “just as He chose us in Him before the foundation of the world, that we would be holy and blameless before Him. In love He predestined us to adoption as sons through Jesus Christ to Himself, according to the kind intention of His will.” God made a plan for mankind before the world was even formed. He knew man would fall, and he created a plan that would bring all of mankind back into harmony with him. As part of that plan, God predetermined that he wanted a group of people to be his children who would help bring the rest of mankind back to perfection. That group is the Church, the body of Christ, or the “us” referred to in the scripture above. God calls individuals to be a part of the Church, but it is up to that individual to accept God’s invitation.
If you are looking for a more in depth study of free will, predestination, and God’s foreknowledge, I would recommend this video: "Elect According to the Foreknowledge of God."