Abstract: Phononic crystal is a kind of periodic structures with the phononic band gap. The dynamically controllable design of its band gap could improve the vibration and noise reduction performance of major equipment in the aerospace field. In the work, smart materials are introduced for band gap design of phononic crystals. And the topological optimization method is used to design the multifunctional phononic crystal with the dynamically controllable band gaps. Firstly, the band gap of phononic crystals are computed by finite element analysis. Simultaneously, the temperature constitutive model of shape memory alloy is established. Secondly, based on variable density method, topology optimization model is established with maximizing the relative band gap under the specific volume ratio and strength constraints. At the same time, the connectivity constraints among phononic crystal unit cells must be ensured. Lastly, the band gaps of multifunctional phononic crystals are optimized by using the moving asymptotic method. During the optimization process, the design sensitivities are calculated with the improved material interpolation model. The optimization results show that the band gap is widened by 103.9% in XY mode with the transformation of shape memory alloy from martensite to austenite. And the bandwidth is increased by 3.75 times in Z mode. This research provides an effective design way for more actively control the phononic crystals band gaps in the complex application environments. And the novel phononic crystals have a wider application prospect.