A technique facilitates the inflow of desired fluids into a downhole well completion while restricting the inflow of undesirable fluids. The technique utilizes at least one autonomous inflow control device which is placed along a well completion to control inflow of fluid from an exterior to an interior of the well completion. The autonomous inflow control device utilizes a plurality of shiftable elements which automatically shift in their relative positions based on the density of fluid in the autonomous inflow control device. This automatic shifting causes the alignment or misalignment of flow openings so as to allow free flow of a desired fluid through the autonomous inflow control device and into the interior of the completion while automatically restricting flow of an undesirable fluid.