We implemented the superadiabatic population transfer within the nonadiabatic regime in a two-level superconducting qubit system.To realize the superadiabatic procedure,we added an additional term in the Hamiltonian,introducing an auxiliary counter-diabatic field to cancel the nonadiabatic contribution in the evolution.Based on the superadiabatic procedure,we further demonstrated quantum Phase and NOT gates.These operations,which possess both of the fast and robust features,are promising for quantum information processing.