The constructions of wavelets or mother wavelet functions are the bases for studying wavelet theory and its application. The different wavelet functions have various properties. Construction of the best wavelet for a given signal and further improvement of the signal processing efficiency and quality are the common aim or interest for theoretical and applied researches. Along with the development of wavelets theory, several methods and their principles and procedures of wavelet construction were discussed in detail. The graphics of scaling function and wavelets function were given with MATLAB 6.0 Language.