With the innovation in computer vision, facial expression recognition (FER) is a dynamic research domain considering extensive practical applications in various domains together with health, education, safety, law enforcement, Banking, marketing, and many more. The researchers have conducted tremendous research work on basic facial expressions recognition, but less on compound emotions recognition, which have complex features due to the combination of basic emotions. Different deep learning models have been used for compound emotions recognition; however, these deep learning models are computationally expensive due to large parameters and training time. To overcome this problem, we have proposed a robust lightweight approach using depthwise separable convolution (DSC), and residual connections. The proposed model outperformed the state-of-the-art (SOTA) models with an achieved accuracy of 70.4% on the RAFDB dataset, and 67.2% on the CFEE dataset. The proposed model improved the accuracy performance of compound emotion recognition by 1.9% on the RAFDB dataset, and 9.8% on the CFEE dataset from the SOTA models. The proposed approach reduced model parameters, and memory consumption compared with the deep learning model of standard convolution.