We propose a novel single-electron refrigerator (SER) which can be fabricated in silicon-on-insulator wafers. The SER has a structure of single-electron box combined with single-electron pump (SEP). An equivalent circuit of the SEP-refrigerator is represented and its stability diagram (Coulomb diamond) is theoretically calculated. It is found that the stability diagram has a honeycomb structure. Moreover, the operation of the single-electron transfer and single-electron storage is numerically demonstrated using a Monte Carlo simulation based on the orthodox theory of the Coulomb blockade phenomenon.