Disclosed are a continuous alternative semiconical roof and a construction method thereof. A roof board is of a structure composed of two groups of continuous semiconical arches, the conical bottoms of the two groups of semiconical arches are respectively perpendicular to opposite-side edges of the roof, the conic nodes are in relative staggered arrangement, the cross section of each group of the semiconical arches is a semicircular arch, the thickness of each semicircular arch increases gradually from the arch crown to the arch bottoms on two sides, the arch bottom of each semicircular arch in one group of semicircular arches and the arch bottom of the adjacent semicircular arch in the other group of semicircular arches are connected to a same support beam, and the ends of the adjacent support beams intersect together and are zigzag on the whole from an overhead view. When the roof is constructed, truss-type arch skeletons which are stable in structure and less prone to deforming are specially made in order to facilitate construction of the arch part, fine wires are arranged between the adjacent arch skeletons to form a whole semicircular arch elevation control network, and construction is facilitated; the method is workable, difficulty in construction is lowered, and a new solving way is opened for modern buildings and construction thereof.