The Lα x-ray production cross sections of Ga, As, Pt, W and Au by electron impact are calculated using a modified version of the BELL formula by incorporating both ionic and relativistic corrections in it. The proposed modified Bell model with a single set of parameters can provide an excellent data in the reduced energy range 1≤E/Inl≤106（E and Inl are, respectively, the incident energy and ionization energy） with performance level at least as good as any of the existing methods and models. Experimental data are compared with the present results in cases of with and without the relativistic correction factor GR and the ionic correction factor Fion, with calculated cross sections obtained from the distorted wave Born approximation and with other experimental data available in the literature. The calculated results can be used to simulate the hot-electron energy spectrum and laser plasma yields and accordingly can provide accurate parameters for electron devices.