Molecular dynamics simulations are performed to investigate phase behavior of a thin film (thickness d~2 nm) of supercooled water confined between two parallel planar walls. In contrast to bulk supercooled water, the confined water, under fixed normal pressures of 0.1 MPa and 500 MPa, does not exhibit the high density amorphous (HDA) to low density amorphous (LDA) liquid-liquid phase transition in the course of the cooling process. A possible explanation is that when the water is confined between two walls, the bulk HDA-LDA phase boundary and the associated critical point C′ shift to lower temperature or/and lower Pzz (confinement pressure) as decreasing the film thickness.