In this work, the effect of electron trapping on the self-similar expansion of electron-ion laser plasma into vacuum, combined with the effect of non-thermal (energetic) electrons is studied. For this, a mono-dimensional, non-relativistic model where the ions are cold and governed by fluid equations is used. In the approximation of quasi-neutrality of charge, the obtained self-similar solution shows that for ion (plasma) behavior, the presence of an important number of non-energetic trapped electrons in the plasma potential wells has the effect of slowing down the expansion, whereas the phenomenon of presence of energetic electrons makes the influence of trapping effect on the self-similar expansion very weak even in the case of a very small number of energetic electrons. This study is of interest in the context of the investigation of mono-energetic ion beams from intense laser interactions with plasmas.