Abstract: The efficient algorithm for evaluating the fractal dimension is the key problem to the implementation of the fractal theory.However，the classical fractal dimension algorithm has become a bottle neck in the application of the fractal theory for its high time and space complexity.Based on Z-ordering technique，the ZBMFD（Z-ordering Based Multifractal Dimension） algorithm is presented.ZBMFD scans the dataset only once to initialize the lowest cell queue and evaluates the fractal dimension of the data set through mapping the lower cells to the higher cells by transforming the coordinate of the lower cells.The elementary time-space complexity of the ZBMFD is presented.Several comparative experiments using synthetic and real life data set show the performance and the effectivity of ZBMFD.