Using molecular dynamic (MD) simulations of the TIP5P model of water, we investigate the effect of hydrophobic confinement on the anomalies of liquid water. For confinement length Lz = 1.1 nm, such that there are 2–3 molecular layers of water, we find the presence of the bulk-like density and diffusion anomaly in the lateral directions. However, the lines of these anomalies in the P–T plane are shifted to lower temperatures (ΔT≈40 K) and pressures compared to bulk water. Furthermore, we introduce a method to calculate the effective diffusion constant along the confinement direction and find that the diffusion anomaly is absent. Moreover, we investigate the hydrogen bond dynamics of confined water and find that the hydrogen bond dynamics preserves the characteristics of HB dynamics in bulk water, such as a non-exponential behavior followed by an exponential tail of HB lifetime probability distributions and an Arrhenius temperature dependence of the average HB lifetime. The average number and lifetime of HBs decrease in confined water compared to bulk water at the same temperature. This reduction may be the origin of the reasons for the different physical properties of confined water from bulk water, such as the 40 K temperature shift.