In the first chapter of Beowulf, Grendel's reasoning behind his attacks on Heorot are explained.
Then an evil creature who dwelt in darkness, full of envy and anger, was tormented by the hall's jubilant revel day by day, as the harps resounded loud, and the song of the singer called out clearly.
Here, readers are made aware that Grendel is both angry and jealous (envy). His anger comes from the "jubilant revel" heard coming from Heorot. While not divulged as to why Grendel is angry and jealous yet, readers know that Grendel is not happy.
The singer sang with the knowledge of tales from man's primeval time: how the Almighty fashioned the earth—a radiant plain rimmed by water—and delighted in its splendor.
The reader is given more information about what Grendel is angry about (given his feelings about the singing). One can infer that Grendel does not like the singing about God and how he has given the people of earth all they need. It is not until the following section that readers come to realize where Grendel's jealousy and hatred stem from.
This accursed one had long dwelled with monsters since the Creator had decreed his exile. On the kin of Cain did the sovereign God avenge the slaughter of Abel; Cain gained nothing from this feud and was driven far from the sight of men for that slaughter. From him awoke all those dire breeds: ogres, elves, and phantoms that warred with God a lengthy while; He paid their wage to them!
Essentially, Grendel is not happy with the fact that he cannot live in the light of God because his ancestors have been exiled. Grendel, given his exile, is not allowed to revel in the light of the world--he cannot take part in celebrations of God in a place like Heorot.
In the end, Grendel's anger stems from the fact that he was born into exile (without having done anything wrong himself). His jealously stems from the fact that he cannot live the same life as those at Heorot.