The time-of-flight mass spectrometer described here has been designed for ions with angle and energy spreads as produced in a real ion source. It performs both transverse and longitudinal focusing. These focusing properties are achieved simultaneously by the inhomogeneous electrostatic field of a rotationally symmetric grid-free ion reflector with conically shaped entrance electrodes. When used in combination with a newly developed longitudinally focusing electron impact ion source, high sensitivity and high mass resolving power are obtained.