In this work, we investigated calcium binding and diffusion on pristine and biaxially strained 2D Sc2C via density functional theory calculations, for potential applications in calcium-ion batteries (CIBs). We found that 2D Sc2C is metallic under PBE, HSE06, and DFT+U approximation conditions, and thus can be potentially used as an electrode material for CIBs. Results showed that pristine 2D Sc2C adsorbs calcium modestly, with relatively low binding energy on the most stable site (0.38 eV). Interestingly, this value shoots up to -1.94 eV and -3.23 eV at 5% and 10% biaxial compressive strains, respectively. Furthermore, calcium's diffusion energy barrier, which is already low (80 meV) on pristine 2D Sc2C, goes down further (to 35 meV) upon application of median biaxial compressive strain (5%). As a result of the enhanced binding of calcium on strained 2D Sc2C, the maximum stable calcium concentration was also boosted. Consequently, the calculated theoretical specific energy capacity of 2D Sc2C with biaxial compressive strain is higher compared to that of the pristine case (878.29 mA h g-1vs. 1051.84 mA h g-1). The average open circuit voltages of the two cases are high and quite close at 9.3 V (pristine) and 9.0 V (with 5% biaxial compressive strain). Our results demonstrated that biaxial compressive strain could be tapped to improve the properties of 2D MXenes, such as Sc2C, thereby enhancing the battery performance indicators of these materials, such as theoretical specific energy capacity and open circuit voltage. Such findings are of great importance in the emerging new technology of CIBs.