We present a scheme for the implementation of three-qubit Grover's algorithm using four-level superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. The scheme is based on resonant, off-resonant interaction of the cavity field with SQUIDs and application of classical microwave pulses. We show that adjustment of SQUID level spacings during the gate operations, adiabatic passage, and second-order detuning are not required that leads to faster implementation. We also show that the marked state can be searched with high fidelity even in the presence of unwanted off-resonant interactions, level decay, and cavity dissipation.