We investigate the effects of nonlinear interactions on quantum diffusion in a quasi-periodic quantum kicked rotor system, featuring a non-Hermitian kicking potential. Remarkably, when the non-Hermitian driving strength is sufficiently strong, the energy diffusion follows a power-laws of time, characterized by an exponent that decreases monotonically as the strength of nonlinear interactions grows. This demonstrates the emergence of super-ballistic diffusion (SBD). We find a distinct prethermalization stage in the time domain preceding the onset of SBD. The unique quantum diffusion phenomena observed in this chaotic system can be attributed to the decoherence effects generated by the interplay between nonlinear interactions and the non-Hermitian kicking potential.