A significant challenge in cardiac tissue engineering is the development of biomimetic grafts that can potentially promote myocardial repair and regeneration. A number of approaches have used engineered scaffolds to mimic the architecture of the native myocardium tissue and precisely regulate cardiac cell functions. However, previous attempts have not been able to simultaneously recapitulate chemical, mechanical, and structural properties of the myocardial extracellular matrix (ECM). In this study, we utilized an electrospinning approach to fabricate elastomeric biodegradable poly(glycerol sebacate) (PGS):gelatin nanofibrous scaffolds with a wide range of chemical composition, stiffness and anisotropy. Our findings demonstrated that through incorporation of PGS, it is possible to create nanofibrous scaffolds with well-defined anisotropy that mimic the left ventricular myocardium architecture. Furthermore, we studied attachment, proliferation, differentiation and alignment of neonatal rat cardiac fibroblast cells (CFs) as well as protein expression, alignment, and contractile function of cardiomyocyte (CMs) on PGS:gelatin scaffolds with variable amount of PGS. Notably, aligned nanofibrous scaffold, consisting of 33 wt. % PGS, induced optimal synchronous contractions of CMs while significantly enhanced cellular alignment. Overall, our study suggests that the aligned nanofibrous PGS:gelatin scaffold support cardiac cell organization, phenotype and contraction and could potentially be used to develop clinically relevant constructs for cardiac tissue engineering.