In this paper we consider the Schrödinger operator L generated inL²(R₊) byy''+q(x)y= µy, x∈R₊:= [0, ∞)subject to the boundary conditiony'(0)-hy(0)=0,where q is a complex valued function summable in [0, ∞ and h≠0 is a complex constant, µ is a complex parameter. We have assumed thatholds which is the minimal condition that the eigenvalues and the spectral singularities of the operator L are finite with finite multiplicities. Under this condition we have given the spectral expansion formula for the operator L using an integral representation for the Weyl function of L. Moreover we also have investigated the convergence of the spectral expansion.