The present invention relates to a wellbore pumping system submerged into a wellbore for unloading liquid from a wellbore comprising well fluid, such as gas, having a wellbore pressure, comprising a pump having an inlet and an outlet, a tubing fluidly connected with the outlet of the pump, and a driving unit connected with and powered by a cable, such as a wireline, and having a rotatable drive shaft for driving the pump, wherein the pump is a reciprocating pump comprising at least one pumping unit having a first moving member displaceable in a housing for sucking well fluid into and out of a first chamber. Furthermore, the invention relates to a wellbore pumping method.