This paper proposes a novel method to reduce computational complexity in two-dimensional (2D) direction of arrival (DOA) angle estimation by utilizing the matrix pencil method with a verti-circular array. The unique geometry of this array eliminates the need for pair matching between azimuth and elevation angles, simplifying the estimation process. The proposed setup consists of two combined sub-arrays: a vertical linear sub-array centered within a circular sub-array. Elevation angles are estimated using the vertical sub-array, which are then used to compute azimuth angles via the circular sub-array. This structure avoids a full-angle search, which is typical for circular and planar arrays. The paper also introduces an enhanced matrix pencil method that incorporates a specialized matrix to reduce noise interference, improving the robustness and overall performance of the technique. Results show a notable decrease in computational complexity, making the method well-suited for real-time signal processing applications.