Lithium niobate on insulator (LNOI) is an emerging photonic platform with great promise for use in future optical communications, nonlinear optics, and microwave photonics. An important integrated photonic building block, active waveguide amplifiers, however, are still missing in the LNOI platform. Here, we report an efficient and compact waveguide amplifier based on erbium-doped LNOI waveguides, achieved using a sequence of erbium-doped crystal growth, ion slicing, and lithography-based waveguide fabrication. Using a compact 5 mm long waveguide, we demonstrate an on-chip net gain of >5dB for 1530 nm signal light with a relatively low pump power of 21 mW at 980 nm. The efficient LNOI waveguide amplifiers could become an important fundamental element in future lithium niobate photonic integrated circuits.