Implementation of high-fidelity swapping operations is of vital importance to execute quantum algorithms on a quantum processor with limited connectivity. We present an efficient pulse control technique, cross-cross resonance (CCR) gate, to implement iSWAP and SWAP operations with dispersively-coupled fixed-frequency transmon qubits. The key ingredient of the CCR gate is simultaneously driving both of the coupled qubits at the frequency of another qubit, wherein the fast two-qubit interaction roughly equivalent to the XY entangling gates is realized without strongly driving the qubits. We develop the calibration technique for the CCR gate and evaluate the performance of iSWAP and SWAP gates The CCR gate shows roughly two-fold improvement in the average gate error and more than 10~\% reduction in gate times from the conventional decomposition based on the cross resonance gate.