Majorana zero modes hold great promise for topological quantum computing. A tunneling current from a metallic probe into a Majorana zero mode gives rise to a zero bias conductance peak. The Majorana peak height is predicted to be robust and quantized at the universal conductance value, 2e²/h. This quantized height is robust and topologically protected from disorder and the tunnel coupling change, which will resolve a quantized conductance plateau when sweeping the corresponding gate voltage. However, all previous reports of Majorana signatures show zero bias peaks with height either much less than, or close but not robust near this quantized value. Here we demonstrate zero bias conductance peaks in Majorana nanowires. The peak height reaches the quantized value 2e²/h for the first time. This peak height stays robust at the quantized value against the tunnel coupling change, giving rise to a quantized Majorana conductance plateau.