We calculated the He atom ground-state energy using a double generalized Laguerre polynomial in the weakest bound electron potential model (WBEPM) theory. An expression for the expectation value of the He atom ground-state energy was derived.We obtained minimumvalues for the He atomground-state energy (Emin). A comparison was made to the results from the Hartree-Fock (HF) method using a double zeta function. Our result was slightly better than the result obtained using a double zeta function in the HF method. We thus show that the linear combination technique can easily be used in WBEPM theory.