The nucleus of our Galaxy is home of several high-energy processes (black hole, intense star formation) that have generated a well-known large scale nuclear wind. We have recently carried out surveys of the Galactic Centre in neutral hydrogen (HI) and CO lines. Our surveys revealed the existence of a population of anomalous high-velocity clouds extending up to heights of about 1.5 kpc from the Galactic Plane. The kinematics of these clouds shows no signature of Galactic rotation and is instead compatible with a bi-conical wind accelerating from the Galactic Centre and reaching a velocity larger than 330 km/s. I will describe the properties of neutral and molecular gas entrained in the nuclear wind, resolved on a ~1 pc scale, and discuss their possible origin. Our data suggest that the Milky Way is expelling up to 0.2-0.3 solar masses of cold gas every year, at a rate comparable to the star formation in the Central Molecular Zone. This outflow may have an important impact on the star formation cycle in the central regions of our Galaxy.