Mechanical waves have a wide range of applications in autonomous soft devices such as mechanical logic gates and microrobots. However, the wave velocity is constant in most systems driven by mechanical waves. This significantly limits the application of mechanical waves in some systems (e.g., soft robots capable of sequence control) that possess a spatial distribution of the heterogeneous energy. In this study, a soft spherical shell array composed of soft-shell elements connected by linear springs is proposed to achieve an adjustable wave velocity. Specifically, the effect of the geometric parameters of a single shell on the energy characteristics is quantified by Finite Element simulations. Theoretical and numerical analyses of the wave properties are also provided. Their results show that adjustable wave propagation behaviors can be designed using the geometrical parameters of the elements. This study provides a basis for the design of energy-efficient soft devices such as soft actuators, controllable energy absorbers and shape-morphing systems.