1. An apparatus for detecting a motion of an image, comprising: a gradient pattern converter for converting a gray level of each pixel in a motion detection area in an input image into a gradient bit pattern by comparing differences between the gray level of the pixel and gray levels of its adjacent pixels with an arbitrary threshold value; and a motion vector detector for forming a search area sequentially in the motion detection area, comparing a gradient bit pattern of the search area with a representative bit pattern of a previous image to calculate and accumulate correlation values, and determining a difference of coordinates of a search area which results in a maximum correlation value and coordinates of the representative bit pattern as a motion vector.