We present a new numerical integrator for molecular integrals that generates automatically an adaptive molecular grid. The tolerance of the numerical integration is the only input parameter of the integrator besides the atomic coordinates and the atomic numbers. The adaptive numerical integrator was successfully implemented in our new density-functional theory method (DFT method) ALLCHEM using the self consistent field (SCF) procedure. The accuracy of the numerical integration is superior to pruned fixed grids for a given number of grid points. The adaptive grid generator allows a very efficient optimization of the grid for an individual molecular system. It is shown that the grid accuracy increases monotonically, if the given tolerance of the numerical integration is decreased. In this way it is possible to obtain results of high numerical precision. For a given tolerance of the numerical integration the adaptive grid generator automatically adjusts the grid to the basis set and the molecular structure. This feature increases the reliability of the numerical integration considerably and the number of expensive reference grid calculations can be reduced. The time for the grid generation is small compared to the total computation time for a SCF calculation.