We report a detailed study of magnetic properties in double perovskite iridate La2ZnIrO6 single crystal, which exhibits an antiferromagnetic (AFM) ground state. The field-and angle-dependent magnetizations [ M(H) and M(phi)] suggest strong magnetic anisotropy in this system. The magnetization of La2ZnIrO6 is isotropic in the ab plane, while it is much stronger than that along the c axis. A field-induced magnetic transition from AFM to ferromagnetic (FM) state is found, which is of a first-order type. The critical behavior is investigated, where critical exponents beta = 0.2317(1), gamma = 0.9783(2), and delta = 5.0071(5) are obtained. The critical exponents belong to the universality class of the tricritical mean-field model, which indicates a field-induced tricritical phenomenon. Based on the scaling equations, we construct the H-T phase diagram for La2ZnIrO6 single crystal with H//b. A tricritical point is revealed at the intersection point between the AFM, FM, and paramagnetic phases (T-tr approximate to 8 K; H-tr approximate to 170 Oe).