The ability to amplify optical signals is of paramount importance in photonic integrated circuits (PICs). Recently, lithium niobate on insulator (LNOI) has attracted increasing interest as an emerging PIC platform. However, the shortage of efficient active devices on the LNOI platform limits the development of optical amplification. Here, we report an efficient waveguide amplifier based on erbium and ytterbium co-doped LNOI by using electron beam lithography and an inductively coupled plasma reactive ion etching process. We have demonstrated that signal amplification emerges at a low pump power of 0.1 mW, and the net internal gain in the communication band is 16.52 dB/cm under pumping of a 974 nm continuous laser. Benefiting from the efficient pumping facilitated by energy transfer between ytterbium and erbium ions, an internal conversion efficiency of 10% has been achieved, which is currently the most efficient waveguide amplifier under unidirectional pumping reported on the LNOI platform, to our knowledge. This work proposes an efficient active device for LNOI integrated optical systems that may become an important fundamental component of future lithium niobate photonic integration platforms.