Semiconductor quantum dot qubits are one of the most promising candidates for quantum computing. Among them, singlet-triplet qubits have attracted much attention due to their excellent properties of all-electric control and accurate readout. To improve qubit immunity to charge noise, strong driving pulses are usually introduced to make operation as fast as possible. However, the complex dynamics induced by strong driving pulses make the rotating wave approximation inapplicable and hinder the implementation of high-fidelity qubit operation. In this work, we present a method of utilizing simple quadrature pulses to correct errors of high-frequency oscillatory terms induced by strong driving. A scheme to obtain these pulses is proposed based on a full quantization of the system and derivative removal by adiabatic gate (DRAG) theory, as the former clarifies the elementary processes of strong driving effects and enables the latter to find correction pulse shapes. The numerical simulation results show that, a NOT gate with 99.99% fidelity and gate time as short as 2 ns can be achieved with the help of the control pulses of this method, which indicates that the control error brought by strong driving is no longer a limiting factor. In particular, NOT gate fidelity higher than 99.9% is achievable even when the charge noise is at a level of $ 2\ \mu{\rm{eV}} $ . Notice that this method can be applied to any resonant-driving single-qubit rotation but not just NOT gates. Therefore, our approach will facilitate qubits to realize fast, high-fidelity single-qubit gates under charge noise.