This paper introduces an algorithm that accurately estimates depth maps using a lenslet light field camera. The proposed algorithm estimates the multi-view stereo correspondences with sub-pixel accuracy using the cost volume. The foundation for constructing accurate costs is threefold. First, the sub-aperture images are displaced using the phase shift theorem. Second, the gradient costs are adaptively aggregated using the angular coordinates of the light field. Third, the feature correspondences between the sub-aperture images are used as additional constraints. With the cost volume, the multi-label optimization propagates and corrects the depth map in the weak texture regions. Finally, the local depth map is iteratively refined through fitting the local quadratic function to estimate a non-discrete depth map. Because micro-lens images contain unexpected distortions, a method is also proposed that corrects this error. The effectiveness of the proposed algorithm is demonstrated through challenging real world examples and including comparisons with the performance of advanced depth estimation algorithms.