A new design of an ion mass spectrometer for the laser-plasma particle diagnostic, which is capable to detect simultaneously also neutral particles, is described. The particles are detected with micro-channel-plate detector operating in a gated mode. This allows us to separate x-rays and energetic electrons from other stray plasma emissions, e.g., neutral particles, which hit the detector in the same place. The ion energies are measured with the spectrometer in energy intervals corresponding to their time-of-flight within the gating window. The latter also defines the energy interval of neutrals recorded with the same time-of-flight. The spectrum of neutral particles can be reconstructed by subsequently collecting different parts of the spectrum while applying different delays on the gate pulse. That separation-in-time technique (time-of-flight mass spectrometry) in combination with the spatially separating mass analyzer (ion mass spectrometer) is used for the neutral particles spectroscopy.