Recent observation of intrinsic ferromagnetism in two-dimensional (2D) CrI3 is associated with the large magnetic anisotropy due to strong spin-orbit coupling of I. Magnetic anisotropy energy (MAE) defines the stability of magnetization in a specific direction with respect to the crystal lattice and is an important parameter for nanoscale applications. In this work we apply the density functional theory to study the strain dependence of MAE in 2D monolayer chromium trihalides CrX3 (with X = Cl, Br, and I). Detailed calculations of their energetics, atomic structures, and electronic structures under the influence of a biaxial strain ɛ have been carried out. It is found that all three compounds exhibit ferromagnetic ordering at the ground state (with ɛ=0), and upon applying a compressive strain, phase transition to the antiferromagnetic state occurs. Unlike in CrCl3 and CrBr3, the electronic band gap in CrI3 increases when a tensile strain is applied. The MAE also exhibits a strain dependence in the chromium trihalides: it increases when a compressive strain is applied in CrI3, while an opposite trend is observed in the other two compounds. In particular, the MAE of CrI3 can be increased by 47% with a compressive strain of ɛ = 5%.