Inter-area oscillations in large power network are poorly controlled via local decentralized control. One promising strategy for wide-area damping of these oscillations is to minimize the quadratic state and control cost function for a linearized system model. In this paper, we improve this linear-quadratic method by introducing novel selective approach. Namely, instead of using the full state we minimize in the cost function only the selected spectral part of the state. The proposed selective LQ optimal problem is reformulated via the selected spectral part of the closed-loop observability Gramian. This spectral part is a solution to the modal Lyapunov equation specially designed for a chosen spectral range. Novel approach allows to take into account in global optimization only the selected set of oscillations and therefore to improve flexibility and accuracy of controllers setting. Numerical experiments with the IEEE New England test system confirm that the selective approach improves the performance of the conventional LQ method for suppressing low frequency inter-area oscillations.