Laser cooling is one of the most promising techniques to reach high phase-space densities for relativistic heavy-ion beams. Preparations for laser cooling of relativistic lithium-like ions, such as C3+ and N4+, are being made at the experimental cooler storage ring (CSRe) in Lanzhou, China. In December 2011, a new buncher was installed and tested with a 70 MeVu(-1) Ne-22(10+) ion beam by electron cooling at the CSRe. The longitudinal momentum spread of the bunched ion beam was measured by the new resonant Schottky pick-up. As a result, Delta p/p approximate to 2 x 10(-5) has been reached at ion numbers less than 10(7). According to this test result, the RF-buncher is suitable for the upcoming experiment of laser cooling at the CSRe. Laser cooling of heavy-ion beams will also be applied at future storage ring facilities, e. g. FAIR in Darmstadt, and HIAF in Lanzhou.