Quantum TUNNELING OF A SUPERCONDUCTOR NANO-GRAIN COUPLED TO A NORMAL METAL IN WEAK MAGNETIC FIELD IS CONSIDERED. BY CONSIDERING THAT DEVIATION OF BCS GAP FUNCTION IS SMALL, THE DOMINANT EQUATIONS OVER THE PERTURBED GREEN FUNCTIONS ARE OBTAINED. THEN, THE MATRIX GREEN FUNCTION IN THE FREQUENCY SPACE IS OBTAINED AND BASED ON IT, THE SELF-CONSISTENT EQUATION OF ORDER PARAMETER CAN BE SOLVED. FINALLY BY USING THE ORDER PARAMETER, THE EVIDENCE OF Quantum TUNNELING transition OF THE SUPERCONDUCTOR NANO-GRAIN IN FREQUENCY SPACE IS ANALYTICALLY CONCLUDED.