The dependence of efficiency of a single step couple impedance jump variation relativistic backward wave oscillator(RBWO) on the relativistic electron beam parameters, couple impedance jump change position and high low couple impedance ratio was analyzed and optimized numerically by means of self consistent RBWO nonlinear theory presented in the paper. The results show that the optimal device efficiency can be up to 50%. A high power X band RBWO with a single step change in the couple impedance was designed and analyzed by using a full electromagnetic particle in cell code to simulate the device output power, efficiency and operating frequency. It was also constructed and investigated experimentally. The efficiency of the device with a single step change in the couple impedance is about twice of the uniform case in the same driving electron beam, beam wave interaction region length and other operating conditions has been achieved in the preliminary experiments.