We report the first hybrid tandem solar cell with solution processable active layers using colloidal PbS quantum dots (QDs) as the front subcell in combination with a polymer-fullerene rear subcell. Al/WO3 is introduced as an interlayer, yielding an open circuit voltage (VOC) equal to about 92% of the sum of the VOC of the subcells. The device exhibits a power conversion efficiency of 1.8%. Optical simulations of various tandem configurations show that combining PbS QDs with small-bandgap polymers is a promising strategy to obtain tandem solar cells with a very broad absorption range and a high short circuit current.