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The exploration of topological phases in carbon allotropes offers a fascinating avenue to realize topological devices based on carbon materials. Here, using first-principles calculations, we propose a novel metastable carbon allotrope, which possesses exotically helical carbon chains bridged by quadrangle-rings. This unique structure with sp2-sp3 bonding networks crystallizes in a noncentrosymmetric face-centered orthogonal (fco) lattice with six atoms in a unit cell, thus named fco-C6. The considerable stability of fco-C6 is confirmed by phonon spectra, elastic constants, and ab initio molecular dynamics simulations. More importantly, fco-C6 exhibits extraordinary electronic properties with the minimum number of Weyl points in a time-reversal preserved Weyl system. The symmetry arguments reveal that the Weyl points are guaranteed to lie along the high-symmetry pathes and thus well separated in momentum space, exhibiting the robustness of topologically protected features. We investigate the topological surface states of fco-C6 projected on a semi-infinite (010) surface. There are only nontrivial Fermi arcs across the Fermi surface, which facilitates their measurements in experiments and further applications in carbon allotropes.