Abstract: Moments factors x^py^q are transformed to function F₁（）by differential operation and image functions f （ i,j） are transformed to function F₂（） by accumulative summation.As‘p’and‘q’in the zeroth and first order moment factors are not larger than 1,so its value is 1 after differential operation. Multiplication by 1 can be omitted.For images of any size and any gray levels,this algorithm needs totally 3 multiplications.Computation result is accurate.Compared with some known methods for gray level image,the new algorithm reduced computational complexity significantly.