A geodesic based approach using Lamb waves is proposed to locate the acoustic emission (AE) source in a composite structure. The approach proposed in this work is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. An AE signal takes this path from its source to an AE sensor array. By propagating the waves in reverse, virtually from these sensors along the minimum energy path and by locating the first intersection point of these waves, one can get the source location. Conventional methods employ triangulation to form distance equations using time-differences obtained from experimental data, which are solved analytically or numerically to get to the location of source. Also, the triangulation approach may not be suitable for complex geometry components and the problem gets compounded if the material of the structure is anisotropic, warranting complex analytical velocity models. The proposed method is more suitable for a practicable source location solution in a more general setup on any arbitrary surface containing finite discontinuities. By allowing the geodesic waves to propagate from multiple sensors (3 or more) and identifying their point of meet, one can obtain a very accurate source location. In an object with discontinuities, a graph theoretical concept can be employed to determine the shortest path on networks using Dijkstra's algorithm, for finding discrete geodesies, which are propagated till the source is reached. The point of intersection is located by employing a construction similar to Voronoi diagram after proving that the intersection point in the diagram provides the location of source. Experiments have been conducted on composite plate specimens of simple and complex geometry to validate this new method.