Staging of plasma accelerators is a critical requirement for high energy particle accelerators or compact colliders. Here we present the first successful demonstration of external injection from a traditional accelerator (Linac) into a LWFA and the subsequent acceleration with ~100% capture efficiency. Stable 31MeV, 20fC electron beams from the Linac were velocity bunched to the length of ~15fs (r.m.s.) in the high-gradient photocathode RF gun and then external injected into the linear wakefield excited by the 10TW, 42 fs laser. The experimental results show that the maximum energy gain can reach to 1.8 MeV in a 6mm long plasma with ~100% capture efficiency, corresponding to an average gradient of about 300 MV/m. High capture efficiency of external injection has also been systematically validated by 3D PIC simulations. The result will pave the way toward the development of a high efficiency high energy particle accelerator.