It reports the investigation on calculation methods of ground-state correlation energy of double-electron system atoms (or ions) by using B-splines basic sets. These methods belong to the application category of calculus of variations, and adopt B-splines techniques to account for the radial bases, and at the same time, deal with the angular bases by using Goldman's mixed L method. The calculation results are given for He, H^-,Li⁺,Be⁺⁺,B⁺⁺⁺ atoms (or ions) and compared with those of others' theoratical methods. This comparison demonstrates that our calculation methods have excellent computing accuracy and efficiency.