The performance of a LaBr3(Ce) gamma spectrometer at high count rates was investigated up to an input count rate of 1.3 Mcps. In order to make its pulse processing faster, a preamplifier provided by the detector manufacturer was eliminated, and the signal from the photomultiplier tube was fed directly to a digital pulse processing system. To accomplish both fast pulse processing and good energy resolution, the pulse-shaping parameters were optimized at a low count rate of 1.5 kcps, and then measurements were carried out at various count rates. Input count rates ranging from 1.5 kcps to 21 kcps were produced using a set of 137Cs resin sources, while higher rates between 45 kcps and 1.3 Mcps were produced using a 1.2-GBq 137Cs source. The spectrometer showed an excellent performance for the input rate up to 150 kcps, while the dead time increased rapidly for the input rates above 150 kcps. The system dead time has been improved greatly by eliminating the preamplifier.