GAMER, a parallel graphic-processing-unit-accerelated adaptive-mesh-refinement hydrodynamic code, has been extended to support magnetohydrodynamics (MHD). The algorithm for MHD is the corner-transport-upwind (CTU) scheme with the constraint transport (CT) technique. The divergent preserving operator for adaptive mesh refinement (AMR) is applied to enforce the divergence-free constraint on the magnetic field. The overall performance banchmarks are conducted to AMD Opteron Processer 6276 (16 processing cores) CPU with Tesla K20X GPU. The uniform grid comparison between GAMER and Athena++, a well-known and widely used pubic code for Astrophysics, is made. It shows that under the same accuracy, GAMER with one GPU is able to achieve about 1/30 computation time of Athena++ with Haswell Xeon E5- 2690v3 which is a 24-processing-cores CPU. Our AMR tests demonstrate that the GAMER’s performance is robust and as good as with the uniform grid case. Furthermore, with the hybrid the message passing interface (MPI)/Open Multi-Processing (OpenMP) parallelization, the computation performance is capable of full exploitation of a heterogeneous CPU/GPU cluster with no latency. Finally, a new stability test problem of a uniform plasma with Arnold-Beltrami-Childress flow (ABC-flow) pattern for the magnetic field is demonstrated for the overall performance examining and it gives some interesting results. Roughly speaking, the system with the longest wave length of the magnetic field is linearly stable and the second longest one is unstable. Furthermore, the unstable one will cast to another stable configuration in which only the largest scale structure appears.