Fear is something that can hold us back in inaction. Fear is something that i have in me regarding my presence and purpose of existence. Apart from my social life, apart from whatever i can do for my family i have an instinct to have much more potential in me. But fear of loosing my present keep me in inaction and i am unable to step forward to my purpose (meaning of my existence). So many doubts and real life barriers are also here. I want to know at what point buddha overcome his (level) fear ? And how it feels to be fearless (completely) ?
Fear is a primal instinct which has its function as it enables us to avoid dangerous situations, thus fearlessness is in itself dangerous and there is such a thing as pathological fearlessness.
Complete and permanent fearlessness came for the Buddha with Awakening, of a different type than pathological fearlessness: for us still shackled by the Hindrances there is only temporary release in the Jhanas and learning to accept fear as part of existence. Moreover, as Acharya Buddharacitta writes, the Buddha taught the Karanya Metta Sutta to his monks in order to help them develop mindfulness as some disgruntled devas were oppressing them with frightful visions:
Monks, go back to the same spot! It is only by striving there that you will effect the destruction of inner taints. Fear not! If you want to be free from the harassment caused by the deities, learn this sutta. It will be a theme for meditation as well as a formula for protection (paritta). Then the Master recited the Karaniya Metta Sutta — the Hymn of Universal Love — which the monks learned by rote in the presence of the Lord. Then they went back to the same place
So that's also a way to deal with fear.
EDIT As others have noted, fear comes from aversion (and this is why the Karanya Metta Sutta dispels fear by replacing it with loving kindness). Thus, the Buddha vanquished fear when he destroyed aversion. This happened before Awakening.
According to the Palicanon-sutras he had to fight with his fears in the seven years of initial life in the homelessness. The key of overcoming the fear was his deep determination to go that path whatever might happen.
I think the "lion's roar" sutta is the one in which he describes something of the process before his awakening (but there are a couple of other suttas dealing with this) and some moments of real fear and anxiousness in the deep and dark forests.
And the "gosingam forest"-sutta closes with his proposal, what makes this forest getting a holy glance: a monk, determined to sit-down and meditate and not to stop before getting the full insight/before destroying the illusion.
So his precept was, just to bear the anxiousness/the fear. When it occurs to look at it: to look inside oneself, to look at the fear how it arises, to breath and to observe the breathing and let go any anxious emotion and look how it goes down again... and steadily proceed on the path.
Fear is an instance of aversion. Aversion is 1 of the 3 roots of evil. You eradicate aversion when you attain the state of Anagami. Buddha attained the state of Anagami before attaining Buddhahod in the last watch of the night on a Vesak full moon Poya day, about 2603 years ago.
To know about how it feels to be completely fearless, read about the life of the Buddha; his encounters with Angulimala the thief, Alavaka the demon. Nalagiri the drunk elephant etc. You can also read stories about Arahaths and Anagamis.