<p>The sensitivity matrix, describing the first-order relationship between the thrust and the change of the orbital elements, has been widely used for solving the finite-thrust orbital transfer problem. However, the sensitivity matrix is often defined with the form of the differential equations hard to be analytically integrated. In this work, to address the limitation of the previous method that the sensitivity matrix necessitates numerical integration, an analytical approach to calculate sensitivity matrix is presented. By expanding each term in the differential equations into Fourier series, the sensitivity matrix can be expressed approximately as an integration of Fourier series, which can be analytically calculated. Subsequently, combining the analytical sensitivity matrix with analytical <i>J</i>₂-preturbed orbital propagator, an analytical approximate piecewise constant thrust solution to finite-thrust orbital transfer problem is presented. Furthermore, through the iterative correction algorithm, the high-accuracy piecewise constant thrust solution to finite-thrust orbital transfer problem can be rapidly obtained. Compared with the high-accuracy sensitivity matrix based on numerical integration, the presented analytical sensitivity matrix maintains comparable accuracy while significantly reducing computational cost for obtaining the piecewise constant thrust solutions, thus it provides a substitution for numerical sensitivity matrix for solving finite-thrust orbital transfer problem.</p>