In this paper we propose a method to solve for an L<sub>q</sub> solution of bundle adjustment, a non-linear parameter estimation problem. Given a set of images of a scene, bundle adjustment simultaneously estimates camera parameters and 3D structure of the scene. Generally, a least squares criterion is minimized by using the Levenberg-Marquardt (LM) method, a non-linear least squares optimization method. It is known that the least squares methods are not robust to outliers, even a single outlier can deviate the solution from its true value. Therefore, we propose a method to minimize an L<sub>q</sub> cost function, for 1 ≤ q <; 2. The L<sub>q</sub> cost function minimizes the sum of the q-th power of errors. The proposed method has an advantage of using the Levenberg-Marquardt (LM) method to find a robust solution of the problem. Our experimental results confirm that the proposed method is more robust to outliers than the standard least squares method.