Although accelerator technology has matured sufficiently, state-of-the-art X-ray linacs for radiotherapy and cargo-scanning capture merely 30-50% of the electrons from a thermionic cathode, requiring a higher cathode current and leaving uncaptured electrons to cause problems due to back bombardment, shortening of cathode life, etc. Any solution to increase capture should be effective, simple, reliable, compact, and low cost in order to be adopted by industry. To address this, we present the design of a 6 MeV high capture efficiency S-band electron linac that captures 90% of the initial DC beam. This linac does not require any extra parts that would increase the cost as the high efficiency is achieved via a low-field-amplitude in the first bunching cell to decrease the number of backstreaming electrons, to velocity bunch the electron beam, and recapture backstreaming electrons. Under the low field amplitude, any electrons launched at decelerating phases travel backward with low speeds, thus most of them can catch the next RF cycle, and get re-accelerated/recaptured. As the electron speed is low, the cell length is also shorter than existing linacs. Such a short field is achieved by the use of asymmetric cells with differential coupling to the side-coupled cells. Our novel design has implications for all commercial high current thermionic gun linacs for increasing beam current and increasing cathode lifetime.