  The quantum Hall effect (QHE) with quantized Hall resistance of h/{\nu}e2
starts the research on topological quantum states and lays the foundation of
topology in physics. Afterwards, Haldane proposed the QHE without Landau
levels, showing nonzero Chern number |C|=1, which has been experimentally
observed at relatively low temperatures. For emerging physics and
low-power-consumption electronics, the key issues are how to increase the
working temperature and realize high Chern numbers (C>1). Here, we report the
experimental discovery of high-Chern-number QHE (C=2) without Landau levels and
C=1 Chern insulator state displaying nearly quantized Hall resistance plateau
above the N\'eel temperature in MnBi2Te4 devices. Our observations provide a
new perspective on topological matter and open new avenues for exploration of
exotic topological quantum states and topological phase transitions at higher
temperatures.
