The helical structure of protein is stabilized by:-

The $\alpha$-helix is the secondary structure of a protein. The polypeptide chain coils into a right-handed spiral.
The helix is held in shape by intramolecular hydrogen bonds between the $C=O$ group of one amino acid residue and the $-NH$ group of the residue four places further along the chain ($C=O \cdots H-N$).
Peptide bonds join the amino acids in the primary structure; they make the chain but do not hold the helix in shape. Ether bonds are not present in proteins.
So the helical structure of a protein is stabilised by hydrogen bonds.