We first present the fabrication technique of apodizing holographic gratings. Gratings with a spatially variable reflectivity profile were obtained by the interference of two Gaussian beams on a glass plate covered with a photoresist. When the exposure time was short enough to avoid saturation of the photoresist, gratings with a quasi-Gaussian reflectivity profile for the beam reflected in the -1 order were produced; the reflectivity at the center could be as high as 71%, and the half-width of the reflectivity profile at the e(-1) position could be as small as 180 mum. Apodizing gratings were used as the end mirror of the external cavity of a broad-area semiconductor laser. Single longitudinal- and lateral-mode operation was observed over the full range of allowed injection currents.