Gaussian filtering is an effective image denoising algorithm, which has been widely used in image processing and computer vision tasks. Existing Gaussian filtering algorithms suffer from low computational efficiency and long execution times. In this paper, we propose RC-Gaussian filtering, an efficient algorithm based on row-column interleaved computation. This algorithm performs interleaved filtering along the rows and columns of image pixels to reduce data reuse distance during computation and enhance memory access efficiency. It also provides an efficient multi-thread mapping strategy and adopts loop tiling and loop unrolling optimizations to improve the computational performance on multi-core processor architecture. The experimental results show that, compared with the classical Gaussian filtering algorithm and an advanced Gaussian filtering algorithm, the proposed algorithm improves the computational efficiency by an average of 1.63 \(\times \) and 1.39 \(\times \) , respectively, across images of varying sizes, while also enhancing filtered image quality. It also outperforms several state-of-the-art deep learning-based denoising algorithms in computational efficiency, achieving speedups ranging from 1.58 \(\times \) to 121.42 \(\times \) .