A Time-of-Flight Mass Spectrometer (TOF-MS) is configured to improve resolution and sensitivity performance. The TOF-MS includes an arrangement of electrodes comprising an ion accelerator with two stages of homogeneous electric fields, an ion reflector with a single stage of a homogeneous electric field, accelerator and reflector being separated by a first drift space, and an ion detector which is separated from the reflector by a second drift space. Contrary to known TOF-MS of similar configuration, the set of electric potentials which must be applied to said electrodes is predetermined for a given geometry in such a way that a spatial distribution of ions initially at rest in the first gap of the said accelerator is compressed at the location of the detector in the longitudinal direction to a focus of first and second order in the initial axial coordinate. Therefore, mass resolution is enhanced over a TOF-MS that provides only for longitudinal focusing of first order, while the number of passages through grid electrodes along the flight path is reduced, and hence ion transmission and instrument sensitivity are improved.