This paper is to investigate self-sustained oscillations of a NACA 0012 airfoil at a transitional Reynolds number using large-eddy simulation (LES). The unsteady compressible Navier-Stokes equations coupled with the Smagorinsky sub-grid scale (SGS) model are solved using a dual time stepping method. The unfactored line Gauss-Seidel relaxation iteration is employed for time marching. The physical temporal terms are discretized using a 2nd-order accuracy backward differencing scheme. To achieve high accuracy, a 5th-order weighted essentially non-oscillatory (WENO) scheme is used for the inviscid fluxes. The viscous terms are discretized using a fully conservative 4th-order or 2nd-order central differencing scheme. A preconditioning method is used for the unsteady computations of the static airfoil at the beginning to generate a good initial solution for the fluid-structural interaction (FSI) computations. A fully coupled fluid-structural methodology is employed. The structurally linear one-degree-of-freedom equation of pitching motion is solved according to the low-amplitude self-sustained oscillations observed in the experiment. All simulations are conducted on a message-passing interface (MPI)-based computer cluster with parallel computations to reduce the wall clock time. The preliminary two-dimensional (2D) LES results show that the developed computational fluid dynamics (CFD)/computational structure dynamics (CSD) simulation is able to capture the self-sustained oscillations with small amplitudes observed in the experiment.