Does the New Testament ever simply refer to Jesus as ‘God’? Absolutely! Though it is not the usual manner of asserting the divinity of Jesus (see here for a discussion of the diverse ways the NT speaks of Jesus as God), yet the NT does on several occasions simply ascribe to him the title ‘theos’ (the Greek word for ‘God’ typically reserved for God the Father).
Many texts are debated as to whether or not Jesus is referred to as theos (θεός), but the ones which most certainly do refer to Jesus as are as follows (taken from the ESV):
John 1.1: In the beginning was the Word, and the Word was with God, and the Word was God.
John 20.28: Thomas answered him, “My Lord and my God!”
Rom 9.5: To them belong the patriarchs, and from their race, according to the flesh, is the Christ who is God over all, blessed forever. Amen.
Titus 2.11-13: For the grace of God has appeared, bringing salvation for all people, training us to renounce ungodliness and worldly passions, and to live self-controlled, upright, and godly lives in the present age,waiting for our blessed hope, the appearing of the glory of our great God and Savior Jesus Christ, who gave himself for us to redeem us from all lawlessness and to purify for himself a people for his own possession who are zealous for good works.
Heb 1.8: But of the Son he says, “Your throne, O God, is forever and ever, the scepter of uprightness is the scepter of your kingdom.
2 Pet 1.1: Simeon a Peter, a servant b and apostle of Jesus Christ, To those who have obtained a faith of equal standing with ours by the righteousness of our God and Savior Jesus Christ.
There are, of course, more texts which are debated, as to whether they refer to Jesus as Theos or not. The ones listed above are, however, the most certain grammatically, logically, and theologically.
I hope that bolsters your faith. The one we worship and serve, the one who saved us, the one for whose return we wait — he is true, Almighty God!
For more discussion on the texts above and several other debated texts, see Murray J. Harris, Jesus As God: The New Testament Use of Theos in Reference to Jesus (Baker Academic, 1998).