A model is presented for the evolution of the galaxy luminosity function in which the distribution of the galaxy masses, star formation time scales, and star formation turn-on redshifts is derived from the initial power spectrum of density fluctuations. The mass function of galaxy halos is very steep at low masses. Star formation occurs quite late, especially for massive galaxies, because it is assumed to begin only when the group surrounding a galaxy has collapsed and tidal encounters commenced. A good fit of the model to the present luminosity function of bright galaxies and to the relation between half-light radius and luminosity for galaxies fainter than M(B) about -21. The predicted relation between halo circular velocity and blue luminosity for bluer galaxies is consistent with the observed Tully-Fisher relation for spiral galaxies. A reasonable fit to the B- and R-band number counts up to B less than 24 is found. The model's main problems are discussed.