Objective: Active control is a critical aspect of adaptive structures. The cable dome structure is a predominant form of large-span spatial architecture, with its equilibrium state representing the interaction between force and form. Consequently, the dome structure is controllable and serves as an ideal model for adaptive structures. Shape memory alloy (SMA), a typical smart material, demonstrates excellent shape memory effects and is frequently utilized as a driving mechanism in active control systems. This article explores the application of SMA in the adaptive cable dome structure to enhance structural form control, improve control accuracy, reduce control complexity and controller weight, and facilitate intelligent control. Methods: This paper uses the Geiger cable dome structure as a case study. First, a three-dimensional finite element model is created using ANSYS APDL software to assess the structural control requirements. Next, uniaxial tensile tests are performed on SMA wires to evaluate their material properties. According to the identified control requirements and the material properties of the SMA wire, a tendon designed for active control is developed and manufactured. A key design criterion is to ensure that the SMA tendon produces a specific plastic strain under load, which must remain below 8%. Subsequently, experimental research is conducted to evaluate the recovery performance of the SMA tendon. The SMA tendon is connected in series with steel wire rope to create the active control unit, which then replaces the external diagonal cables in the cable dome structure for active control testing. The performance of the SMA-based control method is compared with mechanical control methods to assess its effectiveness. Results: When the initial loads were set at 2 000, 2 500, and 3 000 N, the strain in the SMA tendon reached 4.10%, 4.54%, and 4.67%, respectively. Upon heating to 120 ℃, the tendon generated a recovery strain per unit heated length of 0.1462, 0.1554 and 0.1655 m^-1, respectively. Additionally, the rate of recovery strain during heating depended on the martensite volume fraction, which varied with temperature. Compared with mechanical control methods, the cable dome structure controlled by SMA exhibited smaller errors, with smoother curves for internal forces of units and displacements of nodes. Furthermore, the finite element simulation closely aligned with the experimental results, effectively describing the control process of the structure. When the length of the external diagonal cable was shortened by 0.90 mm, the internal force in the structural spine cable increased by more than 25%. Conclusions: This research demonstrates that SMA can function as an active control driver for cable elements in cable dome structures, providing a stable and reliable control process. Compared with mechanical control methods, the SMA control method is more convenient and easier to manage in terms of accuracy; however, the control rate is dependent on the martensite volume fraction. The SMA tendon used in this study is relatively thick, causing temperature transmission from the exterior to the core, which results in a lag effect and requires a certain stabilization time. Adjusting the inclined cables outside the cable dome can effectively control the shape of the cable dome structure and alleviate the relaxation of the spine cables.