The application of CORDIC(COordinate Rotation DIgital Computing) arithmetic in solving transcendental function has become popular in modern engineering. A brief introduction of CORDIC arithmetic was given in this study. Taking the hyperbolic sine and cosine functions as examples, the method of realizing the arithmetic in FPGA was presented and simulated on ISE(Integrated Software Environment) platform. The result showed this arithmetic was of good precision and instantaneity because of using pipeline. This arithmetic has great practical value in some applications. In addition, a curve of the relationship between the iterative number and the error obtained by the Matlab simulation of the arithmetic can help designers planning the number of iterations for practical applications.