A kilowatt laser diode stack pumped solid state heat capacity laser is studied theoretically and fabricated respectively with single slab and double Nd:YAG slabs. Using the theoretical model of heat capacity laser, the output characteristic for a certian time, the relation of the output power, temperature and time, is obtained. The Nd:YAG slab size is 59 mm×40 mm×4.5 mm. The average pump power is 5.6 kW for single slab and 11.2 kW for double slabs, repetition rate of 1 kHz and duty cycle of 20%. In the 1 s running time, the output energy of the laser shows a fluctuation. And the maximal output energy is 1.3 J for one slab laser and 2.06 J for two slabs laser respectedly. After the 1 s process the output energy declines to 70% and 50% of the original values for two lasers respectively. The thermal effects have been minished for one slab cooled by water. The experimental results match well with the calculation data.