Nowadays, Graphics Processing Unit (GPU) is essential for general-purpose high-performance computing, because of its dominant performance in parallel computing compare to that of CPU. There have been many successful trials on the use of GPU in virtualized environment. Especially, NVIDIA Docker obtained a most practical way to bring GPU into the container-based virtualized environment. However, most of these trials did not consider sharing GPU among multiple containers. Without the above consideration, a system will experience a program failure or a deadlock situation in the worst case. In this paper, we propose ConVGPU, a solution to share the GPU in multiple containers. With ConVGPU, the system can guarantee the required GPU memory which the container needs to execute. To achieve it, we introduce four scheduling algorithms that manage the GPU memory to be taken by the containers. These algorithms can prevent the system from falling into deadlock situations between containers during execution.