In this paper we present numerical modelling results for linear time-of-flight mass spectrometers (TOFMSs) with higher-order space focusing. A brief account of the TOFMS theory is given together with optimal geometries and electric fields which provide space focusing condition (i.e. the zero variation in ion time-of-flight caused by a change in initial position). The effect of the initial velocity distribution, a dominating factor that restricts resolution in TOFMSs, on the time-width of a peak in the mass spectrum was demonstrated. The results have shown that the limitations of the mass resolution by different initial velocities of the ions play a significant role in determining the order of space focusing required in practice. At room temperature no significant improvement in the mass resolution can be expected by increasing the order of space focus, because the time spread due to the velocity dispersion and "turn-around" time of the ion with a mass of 100 amu is about ∼ 20 ns. Therefore, the optimum resolving power is about m / Δ m = 200, which is also experimentally measured using a homemade TOFMS. Nevertheless, the theoretical analysis of the space focusing (no thermal energy distribution) is necessary as it provides a reference for judging the importance of velocity distributions, as deviations from the ideal case. © 2010 Elsevier B.V. All rights reserved.