The active damping of the free large oscillations of a satellite on elliptical orbit is discussed. The satellite oscillations are described by non-linear differential equation of second order. According to Pontryagin's principle of maximum the fuel optimal control has piecewise constant form. Solving and fundamental matrix of the differential equation is determined with Erugin's expansion in symbolic form. The problem is reduced to the optimization task with linear quality function and two restrictions. For solving the Sequential Linear Programming method is offered. The ability of the satellite oscillations damping with fuel optimal control is demonstrated by numerical examples.