Development of biocompatible 3D scaffolds is one of the most important challenges in tissue engineering. In this study, we developed polymer scaffolds of different design and microstructure to study cell growth in them. To obtain scaffolds of various microstructure, e.g., size of pores, we used double- and one-stage leaching methods using porogens with selected size of crystals. A composite of poly(3-hydroxybutyrate) (PHB) with poly(ethylene glycol) (PEG) (PHB/PEG) was used as polymer biomaterial for scaffolds. The morphology of scaffolds was analyzed by scanning electron microscopy; the Young modulus of scaffolds was measured by rheometry. The ability to support growth of mesenchymal stem cells (MSCs) in scaffolds was studied using the XTT assay; the phenotype of MSC was preliminarily confirmed by flow cytometry and the activity of alkaline phosphatase and expression level of CD45 marker was studied to test possible MSC osteogenic differentiation. The obtained scaffolds had different microstructure: the scaffolds with uniform pore size of about 125 µm (normal pores) and 45 µm (small pores) and scaffolds with broadly distributed pores size from about 50-100 µm. It was shown that PHB/PEG scaffolds with uniform pores of normal size did not support MSCs growth probably due to their marked spontaneous osteogenic differentiation in these scaffolds, whereas PHB/PEG scaffolds with diverse pore size promoted stem cells growth that was not accompanied by pronounced differentiation. In scaffolds with small pores (about 45 µm), the growth of MSC was the lowest and cell growth suppression was only partially related to stem cells differentiation. Thus, apparently, the broadly distributed pore size of PHB/PEG scaffolds promoted MSC growth in them, whereas uniform size of scaffold pores stimulated MSC osteogenic differentiation.