The density peak (DP) algorithm has been widely used in scientific research due to its novel and effective peak density-based clustering approach. However, the DP algorithm uses each pair of data points several times when determining cluster centers, yielding high computational complexity. In this paper, we focus on accelerating the time-consuming density peaks algorithm with a graphics processing unit (GPU). We analyze the principle of the algorithm to locate its computational bottlenecks, and evaluate its potential for parallelism. In light of our analysis, we propose an efficient parallel DP algorithm targeting on a GPU architecture and implement this parallel method with compute unified device architecture (CUDA), called the ’CUDA-DP platform’. Specifically, we use shared memory to improve data locality, which reduces the amount of global memory access. To exploit the coalescing accessing mechanism of GPU, we convert the data structure of the CUDA-DP program from array of structures to structure of arrays. In addition, we introduce a binary search-and-sampling method to avoid sorting a large array. The results of the experiment show that CUDA-DP can achieve a 45-fold acceleration when compared to the central processing unit based density peaks implementation.