We extend the Fourier transform based method for the analysis of galaxy redshift surveys of Feldman, Kaiser & Peacock (FKP) to model luminosity-dependent clustering. In a magnitude-limited survey, galaxies at high redshift are more luminous on average than galaxies at low redshift. Galaxy clustering is observed to increase with luminosity, so the inferred density field is effectively multiplied by an increasing function of radius. This has the potential to distort the shape of the recovered power spectrum. In this paper, we present an extension of the FKP analysis method to incorporate this effect, and present revised optimal weights to maximize the precision of such an analysis. The method is tested and its accuracy is assessed using mock catalogues of the 2-degree field galaxy redshift survey (2dFGRS). We also show that the systematic effect caused by ignoring luminosity-dependent bias was negligible for the initial analysis of the 2dFGRS of Percival et al. However, future surveys, sensitive to larger scales, or covering a wider range of galaxy luminosities, will benefit from this refined method.