Abstract A computation of the Case A evolution was carried out for the low mass binary system of M 1 + M 2 = 3.9 M⊙. A total of 15 models with different mass ratios and separations were calculated under the conservation assumption. It was found that the evolution of the models can be classified into three types. The results show that the near-contact semi-detached binary systems(NCSs) can be formed by the Case A mass transfer without contact phase, but the range of the initial models is limited. In comparison with the computation results, a statistical study of 29 known NCS systems was made. Two probably evolutionary prospects were discussed for the NCS systems: evolving into contact or getting in detached systems as the post-Algols.