<p>In this work, we propose a structure-preserving algorithm to address a class of gradient flow problems with manifold constraints. At the continuum level, such gradient flow systems satisfy the manifold constraints and the energy dissipation law. These features have posed interesting challenges to the development of numerical methods. We propose a class of time discretization schemes, namely, semi-implicit projection schemes for the numerical solution of this problem. At each time step, the scheme first computes an intermediate numerical solution on the tangent hyperplane of the manifold and then projects it back onto the manifold. We prove that such numerical methods can maintain the manifold constraints and guarantee unconditional energy dissipation, with the help of the Scalar Auxiliary Variable (SAV) approach for general nonlinear models. Numerous experiments are carried out to verify the stability and effectiveness of our method.</p>