Additive manufacturing (AM) method has been a promising technique to produce three-dimensional (3D) tissue engineering scaffolds comprised of complex pore morphologies. Multi-functional scaffolds fabricated through AM techniques can provide outstanding combinations of mechanical and biological properties including stiffness, strength, toughness, and fluidic permeability. Among the various scaffold design methods, the pore morphology based on triply periodic minimal surface (TPMS) has been of great interest to many researchers due to its easy and accurate controllability on design parameters such as pore size, pore shape, volume fraction, and inner channel interconnectivity. In this paper, we propose a new multi-morphology scaffold design algorithm for building a wide variety of complex hybrid scaffolds composed of multiple TPMS morphologies and arbitrarily-shaped transition boundaries within one scaffold using the volumetric distance field (VDF) and the beta growth function (BGF). Through a variety of design results, we demonstrate the potential to design highly complex and heterogeneous scaffolds with enhancements in stiffness, strength, and permeability. In the method, the resulting scaffold hybrid morphology can be easily and accurately controlled to systematically explore a multitude of transition pore morphologies thereby enabling the optimization of multi-functional properties such as a combination of a high mechanical stiffness together with a high biological diffusion rate.