The invention relates to the technical field of design and construction of building structure formwork supports, in particular to a cross beam formwork support and a design and construction method thereof. The design and construction method includes the following steps: firstly, a construction drawing of the cross beam formwork support is designed; secondly, checking of the bearing capacity is conducted; thirdly, the construction drawing is adjusted; fourthly, a beam bottom formwork tray is produced; fifthly, positioning and laying off of vertical rods are conducted; sixthly, a beam bottom formwork support is erected; seventhly, a beam bottom adjustable supporting brace is installed; eighthly, the beam bottom formwork tray is installed; ninthly, a beam bottom formwork main edge is installed; tenthly, beam bottom formwork secondary edges are installed; eleventhly, a beam bottom formwork panel is installed; and twelfth, cross beam reinforcement binding and beam side formwork installationare conducted. According to the cross beam formwork support and the design and construction method thereof, the key technical difficult problem of the vertical and horizontal cross beam bottom formwork main edge elevation difference can be effectively solved, the erection speed of the cross beam formwork support is increased 3 times than that of traditional technologies, factory processing and assembly construction of the beam bottom formwork tray are achieved, the beam bottom formwork tray is recycled hundreds of times, the comprehensive cost of construction can be greatly saved, and the requirements of energy conservation and consumption reduction and green construction are met.