The discovery of the quantum Hall (QH) effect led to the realization of a topological electronic state with dissipationless currents circulating in one direction along the edge of a two-dimensional electron layer under a strong magnetic field(1,2). The quantum anomalous Hall (QAH) effect shares a similar physical phenomenon to that of the QH effect, whereas its physical origin relies on the intrinsic spin-orbit coupling and ferromagnetism(3-16). Here, we report the experimental observation of the QAH state in V-doped (Bi,Sb)(2)Te-3 films with the zero-field longitudinal resistance down to 0.00013 +/- 0.00007h/e(2) (similar to 3.35 +/- 1.76 Omega), Hall conductance reaching 0.9998 +/- 0.0006e(2) / h and the Hall angle becoming as high as 89.993 degrees +/- 0.004 degrees at T = 25 mK. A further advantage of this system comes from the fact that it is a hard ferromagnet with a large coercive field (H-c > 1.0 T) and a relative high Curie temperature. This realization of a robust QAH state in hard ferromagnetic topological insulators (FMTIs) is a major step towards dissipationless electronic applications in the absence of external fields.