Tuning of the electronic bandgap in colloidal quantum dots (CQDs) by changing their size enables the spectral response of CQD-based photodetectors^,,,, and photovoltaic^,,,,,, devices to be tailored. Multi-junction solar cells made from a combination of CQDs of differing sizes and thus bandgaps are a promising means by which to increase the energy harvested from the Sun's broad spectrum. Here, we report the first CQD tandem solar cells using the size-effect tuning of a single CQD material, PbS. We use a graded recombination layer to provide a progression of work functions from the hole-accepting electrode in the bottom cell to the electron-accepting electrode in the top cell, allowing matched electron and hole currents to meet and recombine. Our tandem solar cell has an open-circuit voltage of 1.06 V, equal to the sum of the two constituent single-junction devices, and a solar power conversion efficiency of up to 4.2%.