Fabricating functionally graded scaffolds from biodegradable polymers to enable the mimicking of native tissue is an important challenge. Here we demonstrate the fabrication and utilization of functionally graded non-woven meshes of polycaprolactone incorporated with tricalcium phosphate nanoparticles using a new hybrid twin-screw extrusion/electrospinning (TSEE) process, which allows the time-dependent feeding of various solid and liquid ingredients and their melting, dispersion, deaeration and pressurization together with electrospinning within the confines of a single process. Using this hybrid method, the concentration of tricalcium phosphate nanoparticles could be tailored to vary in a targeted/controlled manner between the two surfaces of the scaffold mesh. The graded scaffolds were seeded and cultured with mouse preosteoblast cells (MC3T3-E1). Within 4 weeks, the tissue constructs revealed the formation of continuous gradations in extracellular matrix with various markers including collagen synthesis and mineralization, akin to the type of variations observed in the typical bone-cartilage interface in terms of the distributions of concentration of Ca particles and of mechanical properties associated with this. The demonstrated hybrid method should allow much better control of the distributions of various ingredients, including the concentrations of drugs/growth factors, as well as the porosity, mechanical property, wettability, biodegradation rate distributions in tissue engineering scaffolds, aiming to mimic the elegant complex distributions found in native tissue.