The deformation of a thin elastic anisotropic plate nonuniform in thickness is considered in a linear approximation. A two-dimensional model of second-order accuracy with respect to the small thickness parameter is constructed for a plate with general-type anisotropy (described by 21 elasticity moduli) via the asymptotic integration of the three-dimensional equations of elasticity theory. A system of differential equations describing the displacements of the middle layer with a differential order coinciding with the order of the Timoshenko-Reissner model is derived. The constructed model is suitable for studying the statics, dynamics, and stability of multilayered and functionally graded plates. The models of second-order accuracy for isotropic plates and plates with partial types of anisotropy were constructed earlier. This is the first time the model of second-order accuracy has been considered for general type anisotropy.