“Believe in God” means to put your trust and hope in God. It is God-centered.

“Believe God” is self-centered. It means that you are the believer of what God says is right. For example, “believe me, tomorrow will rain.” Therefore, 1John 5:10 says that “whoever does not believe God has made Him a liar.”
 

References:

  • Psalm 78:22 “because they did not believe in God and did not trust his saving power.”
  • Titus 3:8 “… those who have believed in God may be careful to devote themselves to good works. …”
  • 1 Peter 1:21 “(you through Christ) are believers in God, who raised him from the dead and gave him glory, so that your faith and hope are in God.”
  • Romans 4:3 “Abraham believed God, and it was counted to him as righteousness.” (Also, Gal. 3:6, James 2:23)
  • 1John 5:10 “Whoever believes in the Son of God has the testimony in himself. Whoever does not believe God has made him a liar, because he has not believed in the testimony that God has borne concerning his Son.”