We present an all-electron implementation of the Gaussian and augmented plane wave density functional method (GAPW method), which allows ab-initio density functional calculations for periodic and non-periodic systems. The GAPW method uses a Gaussian basis set to expand the Kohn–Sham orbitals, whereas an augmented plane wave basis set is introduced as an auxiliary basis set to expand the electronic charge density. The results of the all-electron calculations for a representative set of small molecules are reported to demonstrate the accuracy and reliability of the GAPW method. Furthermore, its performance is shown for some larger systems, including calculations on unbranched alkane chains up to n-C100H202 with 1804 basis functions and a fully hydrated crystalline RNA duplex (sodium guanylyl-3′-5′-cytidine nonahydrate) with 368 atoms and 3168 basis functions. Finally, as a first test an all-electron ab-initio molecular dynamics (MD) run was performed for 32 water molecules in a simple cubic box under ambient conditions. A standard single processor workstation (IBM 397) was used for all the presented calculations.