To prevent a boundary line between blocks from being made visible by successively narrowing lattice intervals presumed on an image, generating lattice point-shaped pixel positions with intervals for each lattice interval, and referring to the whole closest encoded picture elements which are present with equal distances in the surrounding specific directions of the picture elements.

The surrounding specific directions of picture elements are defined as four directions. An image to be encoded storing mechanism 4 stores an image 2 to be encoded, and an encoding level counting mechanism 5 counts encoding levels from the preliminarily decided maximum value to a minimum value 1 in the descending order. A pixel instructing mechanism 6 generates the set of the positions of vertical and horizontal second-dimensional directions of the encoded picture elements in the encoding level instructed by the encoding level counting mechanism 5. A predictive encoding mechanism 7 operates the predictive encoding of the picture elements whose encoding levels are instructed from the maximum value to the minimum value 1 by the pixel instructing mechanism 6, and outputs encoded image data 3. A control mechanism 9 controls the whole multilevel image encoding device 1 including the middle end of the encoding based on an encoding stop signal 8 from the outside part of the encoding device.