We demonstrate low-speckle laser projection using a broad-area vertical-cavity surface-emitting laser (VCSEL) emitting at 840 nm wavelength as the illumination source. By driving the source in a nonmodal emission regime, we were able to achieve speckle contrast values as low as 3.5% in a realistic projection setup. This was done by driving the VCSEL with specific current pulses without using any additional or mechanically moving components to destroy the coherence of the laser beam. We quantitatively model the speckle contrast reduction based on polarization scrambling and the reduced temporal and spatial coherence of the VCSEL.