The calculation of the electronic structure of large systems by methods based on density functional theory has recently gained a central role in molecular simulations. However, the extensive study of quantities like excited states and related properties is still out of reach due to high computational costs. We present a new implementation of a hybrid method, the Gaussian and Augmented-Plane-Wave (GAPW) method, where the electronic density is partitioned in hard and soft contributions. The former are local terms naturally expanded in a Gaussian basis, whereas the soft contributions are expanded in plane-waves by using a low energy cutoff, without loss in accuracy, even for all-electron calculations. For the calculation of excitation energies a recently developed, time-dependent density functional response theory (TD-DFRT) technique is joined with the GAPW procedure. We demonstrate the accuracy of the method by comparison with standard quantum chemistry calculations for a set of small molecules. To highlight the performance and efficiency of GAPW we show calculations on systems with several thousands of basis functions.