Amplitude-preserved Q compensation prestack time migration (Q migration) is a new method that evolved from prestack Kirchhoff time migration (PKTM). Five algorithms are developed for Q migration on graphics processing units (GPUs). First, the principle of Q migration is briefly introduced. Second, one parallel strategy, namely, imaging domain parallel strategy, is proposed to accelerate Q migration on a single GPU by developing GPU algorithm. Results show that the imaging domain parallel strategy with the corresponding algorithm is superior to the CPU algorithm in several aspects, i.e., faster computing speed, shorter computing time, and higher computational efficiency. Third, based on the imaging domain parallel strategy, two division methods, namely, seismic data division method and velocity data division method, are presented to optimize the performance of Q migration on multi-GPUs and four algorithms are implemented by using Message Passing Interface (MPI)+Compute Unified Device Architecture (CUDA) and multi-thread+CUDA. An optimal algorithm is determined by comparing the performance of four algorithms. Results demonstrate that the optimal algorithm has the shortest computing time, which is 3.85 times shorter than that of a single GPU when four GPUs are all involved in computation and 300 times shorter than that of a 4-core central processing unit (CPU). Finally, a parallel computing framework on GPU cluster is established, which consists of imaging domain parallel strategy, seismic data division method and MPI+CUDA. This framework is suitable for all prestack time migration (PSTM) methods and has a short computing time and high speedup ratio on GPU cluster.