We introduce a new coherent anti-Stokes Raman scattering (CARS) suppression scheme based on measuring a non-resonant CARS loss signal by three-beam (pump-Stokes-depletion) double stimulated Raman scattering (SRS) processes, which can be potentially of use for super-resolution Raman microscopy. In the converging configuration with employing both pump-depletion and Stokes-depletion SRS processes, we obtained approximately 94% suppression of non-resonant CARS signal, which is about 1.5 times more efficient than that with the parallel configuration with pump-Stokes and pump-depletion SRS processes. Such an enhanced suppression efficiency in the converging configuration results from a simultaneous loss of photons both in the pump and Stokes beams by double SRS processes, leading to an efficient suppression of the pump-Stokes-pump CARS signal. Based on the present method, we further propose two potential applications: (1) non-resonant background-free CARS imaging and (2) label-free super-resolution Raman imaging, and carry out simple numerical simulations to show their feasibility.