Carbon nanotube reinforced composites are a new type of functional material that meets the needs of high technology fields such as aerospace and medical biology, as well as repeated normal operation in extreme environments. The free vibration and sound insulation characteristics of piezoelectric carbon nanotube reinforced composite (functional gradient carbon nanotube reinforced composites, FG-CNTRC) sandwich plates were studied, which consider a symmetric FG-X distribution and an asymetric FG-V distribution. Based on the third-order shear deformation theory, the dynamic equation and vibro-acoustic equation under four simply supported boundary conditions were established. By using the Navier method and fluid-solid coupling conditions, the natural frequency and the sound insulation were obtained. The correctness and feasibility of the theoretical model were verified through finite element simulation. Then, the influence of parameter changes on free vibration and sound insulation characteristics was discussed. This research provides a theoretical basis for the application of sandwich plates in engineering.