A new type of flexible suspension tension structure (FSTS) is presented in this paper, which has the advantages of high-efficiency, convenient construction and wide application sphere, and it is also a kind of green and low carbon structure. In order to investigate the mechanical behavior of FSTS under the vertical load, series of structures under 10 groups of upward loads and 8 groups of downward loads are calculated with the matrix analysis method. The results show that the passive tensions of cables and displacement in the middle of span present approximate linear features under the downward loads. However, there are double broken linear features in FSTS under the upward loads. So this regularity can be utilized for the simple analysis and two-stage design calculation. Finally, the reliability of FSTS with the initial tension is investigated with the interval method. 81 kinds of structures with different initial tension are calculated, and the influence regularity of the initial tension in the back cable and the bottom cable are given. It is found that the deformation of FSTS is more sensitive to the initial tension of cables. Consequently, the initial tensions of cables are dominated by deformation of structures under design and construction.