In order to solve the high-precision depletion shutdown guidance problem with multiple constraints, this paper proposes an analytical guidance law that can simultaneously consider terminal height, flight-path angle, dynamic pressure constraints, etc. First, a program angle function is constructed with the resultant apparent velocity as the independent variable. Then, the analytical solutions for the height and flight-path angle at the time of depleted shutdown are developed. Finally, by substituting the analytical solution into the terminal constraint equation and using Newton iteration method to solve it, the coefficients of the constructed program angle function can be obtained. The simulation results show that even under the influence of deviations such as engine, mass, aerodynamics, and atmospheric density, the proposed guidance still has high guidance accuracy and robustness.