Novel hybrid organic-inorganic nanostructures fabricated to utilize non-radiative resonant energy transfer mechanism are considered to be extremely attractive for a variety of light emitters for down converting of ultaviolet light and for photovoltaic applications since they can be much more efficient compared to devices grown with common design. Organic-inorganic hybrid structures based on green polyfluorene (F8BT) and GaN (0001) nanorods grown by magnetron sputtering on Si (111) substrates are studied. In such nanorods, stacking faults can form periodic polymorphic quantum wells characterized by bright luminescence. In difference to GaN exciton emission, the recombination rate for the stacking fault related emission increases in the presence of polyfluorene film, which can be understood in terms of Förster interaction mechanism. From comparison of dynamic properties of the stacking fault related luminescence in the hybrid structures and in the bare GaN nanorods, the pumping efficiency of non-radiative resonant energy transfer in hybrids was estimated to be as high as 35% at low temperatures.