A novel class of complex analytic wavelet functions , the wavelet having simple and explicit analytic expression in frequency domain ,is presented based on the method of constructing Bubble wavelet and super-Gaussian spectrum wavelet. Firstly , the conditions of constructing complex analytic wavelets are discussed ,and then the performance of the new wavelets is studied in frequency domain and time domain. According to the method of constructing wavelets , discussed in this paper , a number of complex analytic wavelet functions with different characteristics can be obtained through adjusting a few of control param。ters with loose coupling.