The combined analysis of spectral and lifetime images has the potential to provide more accurate and more detailed information about Förster resonance energy transfer (FRET). We have developed a novel FRET analysis method to analyze images recorded by multispectral lifetime imaging. The new method is based on a phasor approach and facilitates the simultaneous analysis of decay kinetics of donor and acceptor molecules. The method is applicable to both molecules that exhibit a mono-exponential decay and a bi-exponential decay. As an example we show the possibility of extracting the energy transfer efficiency and the fraction of interacting molecules even in the presence of non-interacting molecules. The reliability of the method is investigated by comparing it with conventional FRET-FLIM analyses. We show that, with the same number of detected photons, the spectrally resolved phasor approach provides higher accuracy than other analysis methods; the confidence interval is improved and the FRET efficiency is closer to the real value.