Active control is currently a hot-button issue in the research of reducing vibration and noise created by rolling piston compressors. Active control can effectively suppress the modal vibration of the structure and reduce the modal resonance acoustic radiation. This paper, which focuses on the active control of the compressor shell’s multiple modes with the control of acoustic radiation power being the research objective, studies the relationship between vibration modes and acoustic radiation modes of the compressor shell and the primary sources of noise. An improved Filtered-U least mean square (FULMS) algorithm for compressor vibration and noise control, which is based on the Nesterov accelerated adaptive moment estimation (NADAM) optimization algorithm, is proposed to determine the multi-order modes to be controlled from the perspective of sound energy, and a particle swarm algorithm is used to determine the location and number of secondary sources. The active control model of the compressor shell was established by using the joint simulation platform, and the performance of the improved algorithm was verified and analyzed by the simulation test process. The results show that compared with the traditional FULMS algorithm, the improved FULMS algorithm has better active vibration control effect, higher convergence speed and can effectively suppress structural mode vibration in a short period time.