It is well known that the Galactic bar drives a gas inflow into the Central Molecular Zone , which fuels star formation , accretion onto the central super-massive black hole , and large-scale outflows . This inflow happens mostly through two symmetrical dust-lanes , similar to those often seen in external barred galaxies . Here we use the fact that the Milky Way dust-lanes have been previously identified in ^ { 12 } CO datacubes and a simple geometrical model to derive the first observational determination of the mass inflow rate into the Central Molecular Zone . We find that the time-averaged inflow rate along the near-side dust lane is 1.2 ^ { +0.7 } _ { -0.8 } M _ { \odot } yr ^ { -1 } and along the far-side dust lane is 1.5 ^ { +0.9 } _ { -1.0 } M _ { \odot } yr ^ { -1 } , which gives a total inflow of 2.7 ^ { +1.5 } _ { -1.7 } M _ { \odot } yr ^ { -1 } . We also provide the time series of the inflow rate \dot { M } for the future few Myr . The latter shows that the inflow rate is variable with time , supporting a scenario of episodic accretion onto the Central Molecular Zone .