Force-directed algorithm is one of the most commonly used methods for visualization of 2D graphs. These algorithms can be applied to a plethora of applications such as data visualization, social network analysis, crypto-currency transactions, and wireless sensor networks. Due to their effectiveness in visualization of topological data, various force-directed algorithms for 2D graphs were proposed in recent years. Although force-directed algorithms for 2D graphs were extensively investigated in research community, the algorithms for 3D graph visualization were rarely reported in the literature. In this paper, we propose four novel clustering-based force-directed (CFD) algorithms for visualization of 3D graphs. By using clustering algorithms, we divide a large graph into many smaller graphs so that they can be effectively processed by force-directed algorithms. In addition, weights are also introduced to further enhance the calculation for clusters. The proposed CFD algorithms are tested on 3 datasets with varying numbers of nodes. The experimental results show that proposed algorithms can significantly reduce edge crossings in visualization of large 3D graphs. The results also reveal that CFD algorithms can also reduce Kamada and Kawai energy and standardized variance of edge lengths in 3D graph visualization.