We have developed a picovoltmeter using a Nb dc superconducting quantum interference device for measuring the flux-flow voltage from a small number of vortices moving through a submicron weak-pinning superconducting channel. We have applied this picovoltmeter to measure the vortex response in a single channel arranged in a circle on a Corbino disk geometry. The circular channel allows the vortices to follow closed orbits without encountering any sample edges, thus eliminating the influence of entry barriers.