In a recent image processing system, convolution operations play a significant role in manipulating image and extracting features from images. Due to the increase of kernel sizes, the image processing hardware suffers from severe hardware complexity and power consumption. In this article, an area-efficient structure is proposed for two-dimensional separable convolution operations. Since a separable convolution allows to translate a two-dimensional convolution into two one-dimensional convolutions, it is possible to compute row-wise and column-wise convolutions independently. Whereas the previous work performs such one-dimensional convolutions in sequence, the proposed structure computes the one-dimensional convolutions simultaneously by rescheduling the computational sequence. Experimental results show that the proposed structure saves approximately 80% and 38% of the hardware resources compared to the conventional and previous structures, respectively.