In order to realize flexible organic light emitting diode (OLED), it is critically important to protect moisture and oxygen penetration into the flexible device through the polymer substrates because of intrinsically poor stability of organic materials of OLED to moisture. Since complete protection of the moisture penetration is almost impossible, moisture absorbents are used inside OLED. In this study, metal oxide/polymer hybrid nanofiber with mechanical flexibility and efficient moisture absorption capability was fabricated by electrospinning. Hydrophilic poly(vinyl pyrrolidone) (PVP) or hydrophobic poly(vinylidenefluoride) (PVDF) and calcium oxide (CaO) were used as the fiber forming polymers and as the moisture absorbing particle, respectively. Polymers were first dissolved in appropriate solvents and CaO was then dispersed in the prepared polymer solutions. The hybrid solution was then electrospun, producing the hybrid nanofiber web looking like paper with thickness of about $100{mu}m$. It was observed that all CaO particles were uniformly held by the nanofiber. It was also observed that only a small portion of the surface of CaO particles was covered by fiber since the fiber diameter was much smaller than the CaO particle size. This implied effective moisture absorption through the free surface of CaO. The hybrid nanofiber absorbed moisture very efficiently upto about 70 % of the nanofiber mass. Once moisture was absorbed by the nanofiber, it was never released even at $150^{circ}C$ in vacuum for 2 hours. It is, therefore, expected that the nanofiber may be applied as the flexible thin moisture absorbent to improve stability of the flexible OLED.