We use particle-in-cell simulation to demonstrate that the use of two split intense femtosecond laser pulses can significantly improve the proton energy in the target normal sheath acceleration scheme. By splitting a weak laser pulse from the main laser pulse and irradiating it on the target rear side, the hot electrons are greatly enhanced on both the front and back sides of the solid target, forming a low-density electron layer of a few microns thickness, which in turn further improves the absorption rate of the laser and leads to enhanced acceleration of protons. It is shown that for a wide range of laser intensities, the energy conversion efficiency to protons, the number of high-energy protons, and the cutoff proton energy are almost doubled compared to the single-laser case with the same total laser energy. This simple scheme potentially opens a degree of freedom for manipulating the proton acceleration process and should arouse broad interest due to its wide applications.