To solve the problem that the control force of shape memory alloy (SMA) damper is not adjustable and piezoelectric friction damper is difficult to start up, a novel composite control device whose SMA unit and piezoelectric friction unit work in turn is proposed; and the corresponding electrodynamic property test is carried out. On the basis of the experiment data, BP neural network model for control device is established which takes the sign of velocity, voltage and displacement as input neurons. Results show that the hysteresis curve of the composite control device is full and basically symmetric; and the work performance is stable. As the voltage increases, the area of the hysteresis loop increases gradually, and the energy dissipation capacity increases. At the displacement amplitude of 12mm, the lap energy dissipation in 120V voltage increases by 138.23%, and the equivalent damping ratio increases by 94.23%. The damping device achieved by the combination of two intelligent materials has good energy-dissipating capacity and strong adaptability, and it can be better used for damping control of engineering structures. BP network prediction model can well track the output of the SMA composite control device, and the optimized BP network is more stable and can more quickly get error smaller network model; the neural network algorithm provides a new way for the establishment and application of constitutive model of SMA composite damping device.