Graph analytics systems rely on parallel models to realize parallel processing of large-scale graphs, in which the most extensively used models are the bulk synchronous parallel (BSP) and the asynchronous parallel (AP) model. The BSP model is simple and deterministic but has difficulties in expressing some graph processing algorithms, while the AP model is flexible to handle various kinds of algorithms but behaves inefficiently on memory-intensive algorithms due to higher scheduling overhead and internal global barriers. Additionally, although the matrix computation has demonstrated its high-performance characteristic in graph processing, most matrix-based systems only support the BSP model. To improve efficiency of the AP model for graph analytics, this paper proposes a barrierless AP model which uses matrix operations to process graphs and removes the global barrier in each superstep of the AP model to accelerate the execution progress of algorithms. The proposed model is evaluated by comparing it with both AP and BSP-based systems including GraphLab, GRACE, and GraphMat. Experimental results show that our model behaves better than the asynchronous systems, and even outperforms the BSP-based system on some memory-intensive graph algorithms as well as computation-intensive graph algorithms.