Objective: Parallel imaging accelerates the acquisition of magnetic resonance imaging (MRI) data by acquiring additional sensitivity information with an array of receiver coils resulting in reduced phase encoding steps. Compressed sensing magnetic resonance imaging (CS-MRI) has achieved popularity in the field of medical imaging because of its less data requirement than parallel imaging. Parallel imaging and compressed sensing (CS) both speed up traditional MRI acquisition by minimizing the amount of data captured in the k-space. As acquisition time is inversely proportional to the number of samples, the inverse formation of an image from reduced k-space samples leads to faster acquisition but with aliasing artifacts. This paper proposes a novel Generative Adversarial Network (GAN) namely RECGAN-GR supervised with multi-modal losses for de-aliasing the reconstructed image. Methods: In contrast to existing GAN networks, our proposed method introduces a novel generator network namely RemU-Net integrated with dual-domain loss functions including weighted magnitude and phase loss functions along with parallel imaging-based loss i.e., GRAPPA consistency loss. A k-space correction block is proposed as refinement learning to make the GAN network self-resistant to generating unnecessary data which drives the convergence of the reconstruction process faster. Results: Comprehensive results show that the proposed RECGAN-GR achieves a 4 dB improvement in the PSNR among the GAN-based methods and a 2 dB improvement among conventional state-of-the-art CNN methods available in the literature. Conclusion and significance: The proposed work contributes to significant improvement in the image quality for low retained data leading to 5x or 10x faster acquisition.