Cryocoolers with large cooling powers at 80 K are very promising as they could find important applications in superconducting field such as cooling cables, transformers and fault current limiters. The pulse tube cryocooler has attracted attention due to its virtue of no moving components in the cold region. However, as the cooling power increases, problems inside the thermal buffer tube, such as difficulty in obtaining good flow straightening, existence of Rayleigh streaming, the gravity effect etc., present big obstacles to achieving high thermal efficiency. On the other hand, a free piston Stirling cryocooler, though more complicated due to the existence of the displacer, could avoid these problems with the elimination of the thermal buffer tube. Meanwhile, the efficiency is better than the pulse tube cryocooler around 80 K due to its capability of recovering the acoustic work. In this article, a free piston Stirling cryocooler with about 300 W cooling power at 80 K is designed with our simulation based on thermoacoustic theory. The theoretical analysis and numeric model are given in detail. The phase shift effect of the displacer and the internal energy loss mechanism are discussed. From our calculation, a relative Carnot efficiency of about 50% at 80 K has been obtained analytically.