We put forward a method to easily generate a single or a sequence of fully developed speckle patterns with pre-defined correlation distribution by utilizing the principle of coherent imaging. The few-to-one mapping between the input correlation matrix and the correlation distribution between simulated speckle patterns is realized and there is a simple square relationship between the values of these two correlation coefficient sets. This method is demonstrated both theoretically and experimentally. The square relationship enables easy conversion from any desired correlation distribution. Since the input correlation distribution can be defined by a digital matrix or a gray-scale image acquired experimentally, this method provides a convenient way to simulate real speckle-related experiments and to evaluate data processing techniques.