In traditional image and video coding schemes, separable transforms are typically employed due to their low-complexity implementations. However, the compression efficiency of separable transforms is limited for most natural image/video blocks which generally have arbitrarily directed edge and texture patterns. It is well known that non-separable transforms can achieve better compression efficiency for directional texture patterns, yet they are computationally complex, especially for larger block sizes. In order to achieve higher transform coding gains with relatively low-complexity implementations, in this paper, we propose non-separable secondary transforms (NSSTs). The proposed approach applies a secondary non-separable transform on a sub-block of low frequency coefficients generated using a primary separable transform, such as discrete cosine transform (DCT). Since the proposed NSST is a non-separable transform applied on low frequency coefficients in a much smaller block size, which typically captures most of the signal energy, better coding gains can be achieved with at a relatively low-computational cost. Experimental results show that, compared to the latest HEVC reference software (HM16.6), the proposed method achieves up to a significant 12% coding gain for Intra coding.