This paper proposes an accurate iris localization algorithm for the iris images acquired under near infrared (NIR) illuminations and having noise due to eyelids, eyelashes, lighting reflections, non-uniform illumination, eyeglasses and eyebrow hair etc. The two main contributions in the paper are an edge map generation technique for pupil boundary detection and an adaptive circular Hough transform (CHT) algorithm for limbic boundary detection, which not only make the iris localization more accurate but faster also. The edge map for pupil boundary detection is generated on intersection (logical AND) of two binary edge maps obtained using thresholding, morphological operations and Sobel edge detection, which results in minimal false edges caused by the noise. The adaptive CHT algorithm for limbic boundary detection searches for a set of two arcs in an image instead of a full circle that counters iris-occlusions by the eyelids and eyelashes. The proposed CHT and adaptive CHT implementations for pupil and limbic boundary detection respectively use a two-dimensional accumulator array that reduces memory requirements. The proposed algorithm gives the accuracies of 99.7% and 99.38% for the challenging CASIA-Iris-Thousand (version 4.0) and CASIAIris-Lamp (version 3.0) databases respectively. The average time cost per image is 905 msec. The proposed algorithm is compared with the previous work and shows better results.