An encoding and decoding apparatus using a wavelet transformation and motion estimation is disclosed. The apparatus includes an input module for receiving an image data, a wavelet module for wavelet-transforming the image data received through the input module, an estimation/compensation module, a storage module for storing the image data being transmitted from the input module and transmitting the stored data in a request from the respective modules, an output module for outputting one bit stream by coupling the data being inputted from the wavelet module and a data corresponding to the motion vector being inputted from the storage module, and a control module for controlling operations of the respective modules. According to the present invention, though memories of small amount are used, whole image can be wavelet-transformed and a motion of a block can be estimated in real time when the encoding and decoding a moving picture at real time.