This paper mainly studies the American put option pricing with transaction costs in the CEV process. The specific Crank-Nicolson
form of numerical solution is obtained by the finite difference method. On this basis, Hong Kong stock CKH option is selected as
the object to estimate option price. Finally, by comparing with the actual price, the American put option pricing model is verified
as reasonable. This paper is significant to the rational pricing and the institutional construction of the upcoming stock options in mainland China.