We present the theory, computational implementation, and applications of a density functional Gaussian-type-orbital approach called DGauss. For a range of typical organic and small inorganic molecules, it is found that this approach results in equilibrium geometries, vibrational frequencies, bond dissociation energies, and reaction energies that are in many cases significantly closer to experiment than those obtained with Hartree-Fock theory. On the local spin density functional level, DGauss predicts equilibrium bond lengths within about 0.02 A or better compared with experiment, bond angles, and dihedral angles to within l--2”, and vibrational frequencies within about 3%-5%. While Hat-tree-Fock optimized basis sets such as the 6-3 1 G** set can be used in DGauss calculations to give good geometries, the accurate prediction of reaction energies requires the use of density functional optimized Gaussian-type basis sets. Nonlocal corrections as proposed by Becke and Perdew for the exchange and correlation energies are found to be essential in order to predict bond dissociation energies and reaction energies within a few kcal/mol. The computational efficiency of the present method together with its accuracy, which is comparable to correlated Hartree-Fock based methods, promises a great usefulness of the DGauss approach for the study of large and complex molecular structures.