We report on fabrication of double quantum dots in catalytically grown InAs/InP nanowire heterostructures. In the few-electron regime, starting with both dots empty, our low-temperature transport measurements reveal a clear shell structure for sequential charging of the larger of the two dots with up to 12 electrons. The resonant current through the double dot is found to depend on the orbital coupling between states of different radial symmetry. The charging energies are well described by a capacitance model if next-neighbor capacitances are taken into account.