A motion estimation method for moving picture compression coding that finds a motion vector at a high speed without degrading compression rate and image quality that includes estimating an initial motion point; performing a Newton-Raphson Method (“NRM”) using a Mean Absolute Difference of the estimated motion point as an objective function, and finding a new motion point; determining whether a difference between the new and estimated motion points is less than a minimum error range, estimating the new motion point as the initial motion point when the difference is more than the minimum error range, and performing the NRM; and determining whether a difference between the new and estimated motion points is less than a minimum error range, estimating the new motion point as a final motion point when the difference is less than the minimum error range, and determining a motion vector.