By means of the first-principles calculations, we predict a new metallic two-dimensional carbon allotrope named net W with Cmmm (D¹⁹_2h) symmetry. This new carbon phase consists of squares C₄, hexagons C₆, and octagons C₈, its dynamical stability is validated based on phonon-mode analysis and it is energetically more favored over previously proposed two-dimensional carbon forms such as net C, planar C₄, biphenylene, graphyne, and the recently prepared graphdiyne. On the other hand, we find that net W possesses strong metallicity due to its rather large density of states across the Fermi level contributed by the carbon p_z orbital. Through first-principles molecular dynamics simulations, we theoretically demonstrate that selective dehydrogenation of the parallel-laid narrowest angular polycyclic aromatic hydrocarbons (4-AGNRs) would lead to a spontaneous interconversion to such a net W carbon phase, the possible synthetic routes are also addressed. Of particular interest, semiconductivity could be introduced when a net W carbon sheet is cut into ribbons of certain widths. Our work shows that the net W carbon sheet and its nanoribbons have great potential for future nanoelectronics.