An orbital angular momentum (OAM) fiber amplifier supporting 20 OAM modes based on a ring-core Yb-doped fiber (RC-YDF) is proposed and demonstrated. The RC-YDF we designed and fabricated has two successive Yb-doped annular layers in the ring-core and can support the amplification of OAM (|l|=1, 2, 3, 4, 5) modes at the wavelength of 1064 nm. With a core pump configuration, we characterize the amplification performance of the RC-YDF based amplifier by simulation and experiments. The amplification of each supported OAM mode is proved by the achieved gain of more than 8 dB and a low differential modal gain less than 1dB with an input signal power of about 5dBm. This is the first experimental demonstration, as far as we know, of the amplification of the OAM mode from 1- to 5-order in aYb-doped fiber.