Nonwoven fibrous matrixes have been widely used as scaffolds in tissue engineering, and modification of microstructure of these matrices is needed to organize cells in three-dimensional space with spatially balanced proliferation and differentiation required for functional tissue development. The objective of this study was fabrication of nanofibrous matrix from novel biodegradable poly(p-dioxanone-co-l-lactide)-block-poly(ethylene glycol) (PPDO/PLLA-b-PEG) copolymer, and to examine cell proliferation, morphology of cell–matrix interaction with the electrospun nanofibrous matrix. The electrospun structure composed of PPDO/PLLA-b-PEG fibers with an average diameters of 380nm, median pore size 8μm, porosity more than 80% and mechanical strength 1.4MPa, is favorable for cell–matrix interaction and supports the active biocompatibility of the structure. NIH 3T3 fibroblast cell seeded on the structure tend to maintain phenotypic shape and guided growth according to nanofiber orientation. Good capability of the nanofibrous structure for supporting the cell attachment and proliferation are observed. This novel biodegradable scaffold will be applicable for tissue engineering based upon its unique architecture, which acts to support and guide cell growth.