Let A: D(A)⊂ X → Y be a linear, closed, densely defined unbounded operator, where X and Y are Hilbert spaces. Assume that A is not boundedly invertible. If equation (1) Au=f is solvable, and ‖f_δ-f‖≤δ then the following results are provided. Problem F_δ (u) □(∶=) ‖Au-f‖^2+α‖u‖^2 has a unique global minimizer u_(α,δ) for any f_δ,u_(α,δ)=A^* (AA^*+αI)^(-1) f_δ. There is a function α(δ),lim┬(δ→0)⁡〖α(δ)=0〗 such that lim┬(δ→0)⁡〖‖u_(α(δ),δ)-y‖=0〗, where y is the unique minimal-norm solution to (1). In this paper we introduce the regularization method solving Eq. (1) with unbounded operators. At the same time give an application to the weak derivative operator equation.