Provided are a source driver and a driving method thereof, an array substrate and a display apparatus. The source driver comprises a plurality of output channels, a plurality of output amplifiers corresponding to the plurality of output channels and a bias circuit configured to supply the output amplifiers with bias currents. The driving method comprises: acquiring resistance values of the output channels (101); and for each of the output channels, setting an amplitude of the bias current supplied to the output amplifier corresponding to the output channel from the bias circuit, according to the resistance value of the respective output channel, so that the bias current of the output amplifier corresponding to the output channel with a larger resistance value being greater than or equal to the bias current of the output amplifier corresponding to the output channel with a smaller resistance value in amplitude (102). Amplitudes of bias currents in different output channels are adjusted locally/partly, so that a power consumption of the source driver is decreased under a normal condition for driving and displaying of a display panel and in turn a power consumption of the entire display apparatus is reduced.