Questions & Answers about Я очень голодный после работы.
Russian normally drops the verb быть (to be) in the present tense.
So instead of saying Я есть очень голодный (which is wrong), Russians say:
- Я очень голодный. = I (am) very hungry.
In the past or future, a form of быть appears again:
- Я был очень голодный. – I was very hungry.
- Я буду очень голодный. – I will be very hungry.
Yes, it is natural, especially in everyday spoken Russian.
However, there are a couple of other very common options:
- Я очень голоден. – more “standard”/neutral, slightly more literary.
- Мне очень голодно. – literally “It is very hungry to me” → I feel very hungry.
All three are correct; the one in your sentence is just more colloquial and personal in tone.