Complementary information obtained from multiple contrasts of tissue facilitates physicians assessing, diagnosing and planning treatment of a variety of diseases. However, acquiring multiple contrasts magnetic resonance images (MRI) for every patient using multiple pulse sequences is time-consuming and expensive, where, medical image synthesis has been demonstrated as an effective alternative. The purpose of this study is to develop a unified framework for multimodal MR image synthesis. A unified generative adversarial network consisting of only a single generator and a single discriminator was developed to learn the mappings among images of four different modalities. The generator took an image and its modality label as inputs and learned to synthesize the image in the target modality, while the discriminator was trained to distinguish between real and synthesized images and classify them to their corresponding modalities. The network was trained and tested using multimodal brain MRI consisting of four different contrasts which are T1-weighted (T1), T1-weighted and contrast-enhanced (T1c), T2-weighted (T2), and fluid-attenuated inversion recovery (Flair). Quantitative assessments of our proposed method were made through computing normalized mean absolute error (NMAE), peak signal-to-noise ratio (PSNR), structural similarity index measurement (SSIM), visual information fidelity (VIF), and naturalness image quality evaluator (NIQE). The proposed model was trained and tested on a cohort of 274 glioma patients with well-aligned multi-types of MRI scans. After the model was trained, tests were conducted by using each of T1, T1c, T2, Flair as a single input modality to generate its respective rest modalities. Our proposed method shows high accuracy and robustness for image synthesis with arbitrary MRI modality that is available in the database as input. For example, with T1 as input modality, the NMAEs for the generated T1c, T2, Flair respectively are 0.034±0.005, 0.041±0.006, and 0.041±0.006, the PSNRs respectively are 32.353±2.525dB, 30.016±2.577dB, and 29.091±2.795dB, the SSIMs are 0.974±0.059, 0.969±0.059, and 0.959±0.059, the VIF are 0.750±0.087, 0.706±0.097, and 0.654±0.062, and NIQE are 1.396±0.401, 1.511±0.460, and 1.259±0.358, respectively. We proposed a novel multimodal MR image synthesis method based on a unified generative adversarial network. The network takes an image and its modality label as inputs and synthesizes multimodal images in a single forward pass. The results demonstrate that the proposed method is able to accurately synthesize multimodal MR images from a single MR image.