In textbooks of《Analysis》, it usually solves improper integral with parameter through derivation in the presentation of integration and exchanging the order of integral. But those methods seem disabled in some of improper integral with parameter, such as and so on. This paper will solve the improper integral with parameter above on the methods of Fourier transform，from cut-in sine function、cut-in cosine function and two-sided exponential function. Meanwhile, it gives the result of a class of relating improper integral with parameter.