In this paper, we consider an inverse source problem of identification of F(t) function in the linear parabolic equation u(t)=u(xx)+F(t) and u(0)(x) function as the initial condition from the measured final data and local boundary data. Based on the optimal control framework by Green's function, we construct Frechet derivative of Tikhonov functional. The stability of the minimizer is established from the necessary condition. The CG algorithm based on the Frechet derivative is applied to the inverse problem, and results are presented for a test example. Copyright (c) 2014 John Wiley & Sons, Ltd.