The steered response power with phase transform (SRP-PHAT) algorithm is widely used for sound source localization due to its strong robustness in reverberant environments. However, the traditional SRP-PHAT algorithm has insufficient localization accuracy and large computational volume in multi-microphone array source localization scenarios, which cannot meet the demand for high-precision real-time source localization. Aiming at the above problems, a SRP-PHAT algorithm based on quadratic cross-correlation is proposed. In this approach, the autocorrelation and cross-correlation between the signals of two groups of channels in the array are subjected to quadratic cross-correlation. The generalized cross-correlation phase transform function (GCC-PHAT) is used as the basis for further calculation to obtain the improved SRP-PHAT function, followed by peak detection to achieve sound source localization with improved accuracy. To reduce computational load, the microphone array is divided into reference channels and sound source channels, and correlation operations are performed only between these groups. This avoids the redundancy of traditional pairwise computations across all channels, significantly lowering the computational cost. The traditional SRP-PHAT algorithm and the SRP-PHAT algorithm based on quadratic inter-correlation are transplanted in the self-developed 128-array multi-spiral-arm array source localization system, and the experiments of source localization are conducted indoors at four source frequencies (10~25 kHz). The experimental results show that the improved algorithm reduces the azimuth estimation error by an average of 2.5°, the pitch estimation error by an average of 2°, and the spatial resolution of the localization by an average of 45.78% for the localization of sound sources at four different source frequencies. Compared with the conventional algorithm, the improved algorithm improves the localization accuracy and reduces the computation amount significantly, which provides an effective solution for the SRP-PHAT algorithm for real-time sound source localization in multi-microphone arrays.