A semiconductor package with enhanced mobility of ball terminals is revealed. A chip is attached to the substrate by a die-attaching material where the substrate has at least a stepwise depression on the covered surface to make the substrate thickness be stepwise decreased from a central line of the die-attaching area toward two opposing sides of the substrate. The die-attaching material is filled in the stepwise depression. Therefore, the thickness of the die-attaching material under cross-sectional corner(s) of the chip becomes thicker so that a row of the ball terminals away from the central line of the die-attaching area can have greater mobility without changing the appearance, dimensions, thicknesses of the semiconductor package, nor the placing plane of the ball terminals. Accordingly, the row of ball terminals located adjacent the edges or corners of the semiconductor package can withstand larger stresses without ball cracks nor ball drop. The stepwise depression can accommodate the die-attaching material to control bleeding contaminations.