Abstract: In practice, the signals being analyzed are often very far from regular or smooth, and these irregular signals usually have many non-differentiable points, even nowhere differentiable. To describe the signal whose pointwise singularity varies along the sample path, in terms of the concept of multifractal, a new algorithm based on discrete wavelet transform for synthesis of multifractional Brownian motion was proposed. The desired local regularity of the multifractional process was obtained by controlling the weights of the wavelet expansion of the Gaussian white noise. The convergence of the synthesized process was controlled by an experimental factor. Compared with both Durbin-Levinson model and circulant matrix embedding model, this algorithm is not only time saving, but also appropriate for generating the multifractional process that is non-Gaussian and autocovariance function unknown in advance. The validity and rationality were verified by numerical experiments.