Chaotic system is widely applied in field of information security because of its excellent properties of unpredictability, no periodicity, pseudo-randomness, and high sensitivity to initial parameters. In this paper, we propose a new chaotic map, named 2D arcsine and sine combined logistic map (2D-ASLM), which is a combination of arcsine, Sine, and Logistic maps. Compared with the existing chaotic maps, the proposed one has the better pseudo-randomness and ergodicity from the viewpoint of chaotic performance. Besides, it also has a more unpredictable chaotic rang as well as a relatively low implementation cost. A chaotic tree transform (CTT) is introduced to effectively disrupt the image pixel positions. Then, the image can be encrypted by combining 2D-ASLM and CTT. Extensive results on encryption simulation and security analysis have shown the effectiveness of the proposed algorithm from different aspects.