We study transition from regular to chaotic motion in the neighbourhood of stable equilibrium point of a relativistic current-carrying string-loop located around Schwarzschild black hole. We demonstrate successive transfer from the purely regular, periodic motion through quasi-periodic motion to purely chaotic motion of the string loop, with increasing of its energy. We also calculated quasi-periodic fundamental frequencies, which are important for survival of corresponding KAM tori. Using maximal Lyapunov exponent we show how the chaoticity of the string loop motion changes with increase of the string loop energy.