Multi-contrast MRI images use different echo and repetition times to highlight different tissues. However, not all desired image contrasts may be available due to scan-time limitations, suboptimal signal-to-noise ratio, and/or image artifacts. Deep learning approaches have brought revolutionary advances in medical image synthesis, enabling the generation of unacquired image contrasts (e.g., T1-weighted MRI images) from available image contrasts (e.g., T2-weighted images). Particularly, CycleGAN is an advanced technique for image synthesis using unpaired images. However, it requires two separate image generators, demanding more training resources and computations. Recently, a switchable CycleGAN has been proposed to address this limitation and successfully implemented using CT images. However, it remains unclear if switchable CycleGAN can be applied to cross-contrast MRI synthesis. In addition, whether switchable CycleGAN is able to outperform original CycleGAN on cross-contrast MRI image synthesis is still an open question. In this paper, we developed a switchable CycleGAN model for image synthesis between multi-contrast brain MRI images using a large set of publicly accessible pediatric structural brain MRI images. We conducted extensive experiments to compare switchable CycleGAN with original CycleGAN both quantitatively and qualitatively. Experimental results demonstrate that switchable CycleGAN is able to outperform CycleGAN model on pediatric MRI brain image synthesis.