Abstract: We investigate the electronic transitions X 1Σ+g → b 3Σu+, X 1Σ+g → a 3Σg+, and X 1Σ+g → B 1Σu+ of molecular hydrogen by studying electron impacts in astrophysical Lorentzian plasmas. Useful fitting formulae for the X 1Σ+g → b 3Σu+, X 1Σ+g → a 3Σg+, and X 1Σ+g → B 1Σu+ excitation cross sections are employed in order to obtain the electronic excitation rate coefficients of H2 as functions of the spectral index and temperature. In low-temperature regions, it is found that the excitation rate coefficients , , and of H2 in non-Maxwellian plasmas are smaller than those in Maxwellian plasmas. However, in high-temperature regions, the excitation rate coefficients of H2 in non-Maxwellian plasmas are greater than those in Maxwellian plasmas. It is also shown that the X 1Σ+g → b 3Σu+ excitation rate coefficient is the main contributor in low-temperature regions. In contrast, it is found that the X 1Σ+g → B 1Σu+ electronic excitation is dominant in high-temperature regions.