In this paper, we have proposed the design of all-optical AND logic gate using the combination of universal NAND gates. The structure consists of hexagonal arrangement of air holes in silicon. The proposed structure has been designed using the finite difference time domain (FDTD) method. The optimized NAND gates have been arranged in a combination such that the combined structure behaves as an all-optical AND logic gate. The proposed structure exhibits a response period of 6.48ps and bit rate of 0.154 Tb/sec.