<p>In optimization problems with complex or unknown gradients, using a derivative-free algorithm is an efficient approach. In this paper, we present a new derivative-free optimization method designed for problems in which the search space is a Riemannian manifold. The method utilizes a simplex gradient approximation and incorporates a line search strategy. We state the conditions under which the proposed algorithm is well-defined and establish its convergence to critical points on Riemannian manifolds from any starting point. Lastly, we demonstrate the practical implementation of this technique on two commonly used manifolds and compare its performance to some existing Riemannian derivative-free methods.</p>