The reasonable dissociation limit of the A1∑+ state 7LiH molecule is obtained. The accurate dissociation energy and the equilibrium geometry of this state are calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space for the first time. The whole potential energy curve and the dipole moment function for the A1∑+ state are calculated over a wide inteuclear separation range from about 0.1 to 1.4 nm. The calculated equilibrium geometry and dissociation energy of this potential energy curve are of Re=0.2487 nm and De=1.064 eV,respectively. The unusual negative values of the anharmonicity constant and the vibration-rotational coupling constant are of wexe=-4.7158cm-1 and αe=-0.08649cm-1, respectively. The vertical excitation energy from the ground to the A1∑+ state is calculated and the value is of 3.613eV at 0.15875nm (the equilibrium position of the ground state).The highly anomalous shape of this potential energy curve, which is exceptionally flat over a wide radial range around the equilibrium position, is discussed in detail. The harmonic frequency value of 502.47cm-1 about this state is approximately estimated. Careful comparison of the theoretical determinations with those obtained by previous theories about the A1∑+ state dissociation energy clearly shows that the present calculations are much closer to the experiments than previous theories, thus represents an improvement.