Semiconducting polymers are very promising optoelectronic materials enabling the simple fabrication of devices such as light-emitting diodes, lasers and solar cells. However, the development of polymer lasers has been hampered by the low charge mobility of these materials preventing electrically driven lasers. We find that this problem can be overcome by taking advantage of the complementary properties of inorganic semiconductors. We show that by separating the charge transporting and lasing regions in a structure combining an indium gallium nitride light-emitting diode with a semiconducting polymer distributed feedback laser, an electrically pumped hybrid polymer laser can be made. This provides a new route to simple, convenient, compact and low-cost visible lasers with the potential for applications in security, sensing, spectroscopy, and medical diagnostics.