A horizontally arranged six-degree-of-freedom constant-stiffness mechanism is provided, and includes an upper platform, a bottom plate, three composite spherical hinges, spherical hinges, support rods, guide rail slider assemblies, and six electromagnetic adjustable stiffness units. Two ends of a shaft on which a permanent magnet is fixed in each electromagnetic adjustable stiffness unit are fixed to the bottom plate via shaft supports. Axially moving housings of electromagnetic adjustable stiffness units are fixed on sliders of the guide rail slider assemblies via slider backing plates respectively. Guide rail slider assembles are fixed on the bottom plate. Tops of the housings are mounted with the spherical hinges respectively. A bottom of the upper platform is uniformly mounted with the composite spherical hinges. One end of each support rod is threadedly connected to a corresponding one of the spherical hinges, and another end is connected with a corresponding one of composite spherical hinges.