This paper presents a novel approach to accelerate the 2D Mallat decomposition algorithm. In particular the proposed approach performs the 2D Mallat decomposition algorithm by way of computing the 2D cyclical convolution, and further completes the 2D cyclical convolution with the fast number theoretical transform (FNTT). Therefore, the 2D Mallat decomposition algorithm can be speeded up. The results obtained from the theoretical analysis and the experiment show that the 2D Mallat decomposition algorithm is significantly improved.