For efficient storage and transmission of medical images, the requirement of image com pression is increasing. Because differences between reconstructed images and original images are related with errors In the diagnosis, lossless compression is generally preferred in mod- ical images. in Run Length Coding which is one of the lossless compression method, we have applied modified scanning direction based on the Hilbert curve, which is a kind of space fill ins curve. We have substituted the traditional raster scanning by Hilbert curve direction scanning. Using this method, we have studied enhancement of compression efficiency for medical images.