The dynamic sparse approximate inverse (SPAI) preconditioner has proven to be effective in accelerating the convergence of iterative methods for large linear systems. Recently, accelerating it on graphics processing unit (GPU) has attracted considerable attention due to the fact that the cost of constructing the preconditioner is high. However, the existing parallel dynamic SPAI preconditioning algorithms on GPU are usually ineffective because of the out-of-memory error for large matrices. This motivates us to investigate how to accelerate the construction of dynamic SPAI preconditioners on GPU. In this article, we propose an efficient dynamic SPAI preconditioning algorithm on GPU, called GDSPAI. For our proposed GDSPAI, there are the following novelties: (1) a well-known dynamic SPAI preconditioning algorithm is substantially modified to address the main challenges of parallelization on GPU, (2) a parallel framework of constructing the dynamic SPAI preconditioner on GPU is presented on the basis of the modified dynamic SPAI preconditioning algorithm; and (3) each component of the preconditioner is computed in parallel inside a group of threads. Experimental results show that the proposed GDSPAI is effective for large matrices, and outperforms the popular preconditioning algorithms in three public libraries, as well as a recent parallel static SPAI preconditioning algorithm.