What mantra can I chant when I feel anxious or afraid?

any name of God you love, chanted slowly with the breath — Hanumān Chālīsā and “Om Namaḥ Śivāya” are popular choices.

Tradition offers many anchors for a frightened mind. The Hanumān Chālīsā is perhaps the most loved — its lines promise that ghosts and fears do not come near one who remembers Mahāvīra. Others chant “Om Namaḥ Śivāya”, “Śrī Rāma Jaya Rāma Jaya Jaya Rāma”, the Mahāmṛtyuñjaya mantra, or “Om Duṁ Durgāyai Namaḥ”.

What helps most is the method: sit or lie down, slow your breathing, and chant softly so the out-breath becomes longer than the in-breath. Hold a mālā if you have one; the physical counting also steadies the mind. Even a few minutes can ease the wave.

Prayer is a real support, but anxiety that is frequent, intense or disturbs sleep and work deserves professional care, just like any other health concern. Talking to a doctor or counsellor and continuing your prayers go perfectly well together.

Slow, longer out-breath calms the body · Source: common devotional practice

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