We propose a scheme for laser cooling of negatively charged molecules. We briefly summarize the requirements for such laser cooling and we identify a number of potential candidates. A detailed computation study with C_{2}^{-}, the most studied molecular anion, is carried out. Simulations of 3D laser cooling in a gas phase show that this molecule could be cooled down to below 1 mK in only a few tens of milliseconds, using standard lasers. Sisyphus cooling, where no photodetachment process is present, as well as Doppler laser cooling of trapped C_{2}^{-}, are also simulated. This cooling scheme has an impact on the study of cold molecules, molecular anions, charged particle sources, and antimatter physics.