This paper examines the pricing of barrier options when the underlying asset follows the constant elasticity of variance (CEV) process. We construct a trinomial method to approximate the CEV process and use it to price barrier options, and demonstrate the accuracy of our approach for different parameter values of the CEV process. We find that the prices of barrier options for the CEV process deviate significantly from those for lognormal process. For standard options, the corresponding differences between the CEV and Black Scholes models are relatively smal1．The result mode1 specification for options depends an extrema than for standard option．