Calcium ion is the ubiquitous messenger in cells and plays a key role in neuronal signaling and fusion of synaptic vesicles. These vesicles are typically ~20-50 nm in diameter and thus their interaction with calcium ions cannot be modelled faithfully with a conventional flat membrane bilayer setup. Within our newly developed molecular dynamics simulations setup, we characterize here interactions of the calcium ion with curved membrane interfaces with atomistic detail. The present molecular dynamics simulations together with time-dependent fluorescence shift experiments suggest that the mode and strength of interaction of calcium ion with a phospholipid bilayer depends on its curvature. Potential of mean force calculations demonstrate that the binding of calcium ion to the positively curved side of the bilayer is significantly stronger compared to that to a flat membrane.