We demonstrate a high efficiency multi-kW diode-side-pumped Nd:YAG laser. High cooling efficiency of the diode-side-pumped module in the laser is achieved. The middle portion of the Nd:YAG rod in the module is cooled by a coolant jet with screwed side surface, and the end-caps of the rod without screwed side surface are cooled by Au coated on the surface. The thermal effect of the laser rod is reduced, which leads to high output power with high optical-optical conversion efficiency. By using three identical Nd:YAG laser modules, an output power of 4.2 kW and beam quality of 58 mm?mrad with an optical-optical efficiency of 35%at 1064 nm is obtained in a laser oscillator. By using four identical Nd:YAG laser modules, an output power of 3.1 kW and beam quality of 17 mm?mrad with an optical-optical efficiency of 25.8%is demonstrated in a master oscillator power-amplifier system.