Computational ghost imaging (CGI) has been widely studied owing to its high resolution and robustness. In contrast with traditional imaging schemes, CGI requires large amount of measurements to be taken for reconstructing a single image; thus, the efficiency of CGI needs to be improved. In this context, wavelet transform has attracted much attention because it can better decorrelate and then significantly compress a signal. By introducing Haar wavelet transform into the CGI scheme, the imaging speed has been significantly improved. However, because of the presence of various types of wavelets with different features, the application of other wavelets in the CGI scheme is scarcely reported. Because many wavelets are unorthogonal, they can only perform continuous wavelet transform, which may bring problems when applying them to the CGI scheme. Thus, a semicontinuous wavelet transform scheme was proposed. A CGI based on Mexihat and Gauss wavelets (both in 1D and 2D) were experimentally realized. The experimental results show that the two continuous wavelet schemes can perform normal imaging and show stronger antiinterference ability than Haar wavelet, which are more suitable for practical applications.