A thick matter pump with a conveying chamber which extends along a closed path from an inlet opening via an outlet opening back to the inlet opening, with the result that the conveying chamber forms a first connecting path and a second connecting path between the inlet opening and the outlet opening. A first piston performs a conveying movement along the first connecting path of the conveying chamber, with the result that, by way of the conveying movement, thick matter is conveyed out of the conveying chamber through the outlet opening, and thick matter is introduced through the inlet opening into the conveying chamber. A shut-off element is arranged in the conveying chamber, which shut-off element, in a first state, shuts off the second connecting path and, in a second state, opens the second connecting path in order to permit a movement of the first piston along the second connecting path. Moreover, the invention relates to a method for conveying thick matter.