A high-efficiency form-finding algorithm is crucially important for finding a stabilized tensegrity structure. In this paper, a modified Broyden-Fletcher-Goldfarb-Shanno noise-tolerant zeroing neural network (MBFGS-NTZNN) form-finding approach is developed and investigated for the form-finding problems of tensegrity systems. A modified BFGS algorithm (MBFGS) is employed to solve the irreversibility of the Hessian matrix, which could avoid the non-positive definite circumstance of the stiffness matrix. Additionally, the approach could be utilized to make a reduction in algorithm calculation complexity. Moreover, to find a group of suitable nodal coordinates, a zeroing neural network (ZNN) based NTZNN is considered to suppress the noise, which may include rounding errors and external disturbance during the form-finding process. Besides, the 0-stable and global convergence under the pollution of noise are verified. Eventually, numerical simulations and an application example are conducted to ascertain the superiority and availability of the MBFGS-NTZNN algorithm in the fields of form-finding.