The aim of this study is to develop a facile and efficient process to provide electrospun poly(ɛ-caprolactone) (PCL) scaffold with a bone-like calcium phosphate (CaP) coating while maintaining its fibrous and porous structure. Firstly, PCL scaffolds with uniform fibrous structure were fabricated by electrospinning. Before CaP coating, a plasma surface treatment was applied to clean and activate the PCL surface for calcium and phosphate ion grafting. Then, the treated PCL scaffolds were immersed in 10× simulated body fluid (SBF10) for varying time periods. PCL fibers were found to be mineralized after immersion in SBF10 for 2 h (SBF10_2h). After 6 h, the PCL scaffolds (SBF10_6h) were fully covered with CaP coating and the porous structure was lost. The coating of SBF10_2h was determined to consist of a mixture of nano-apatite and dicalcium phosphate dihydrate (DCPD). By continuous immersion in classical SBF for 7 days, the coating transformed into pure calcium deficient type B carbonate apatite with nano-crystallinity, which was similar to biological apatite. The deposited calcium phosphate coatings improved the wettability of the electrospun PCL scaffold. As the mineralized electrospun scaffold has a similar structure as the natural bone, it is expected to be a potential cell carrier in bone tissue engineering.