This paper presents a novel 3D indoor Laser-aided Inertial Navigation System (L-INS) for the visually impaired. An Extended Kalman Filter (EKF) fuses information from an Inertial Measurement Unit (IMU) and a 2D laser scanner, to concurrently estimate the six degree-of-freedom (d.o.f.) position and orientation (pose) of the person and a 3D map of the environment. The IMU measurements are integrated to obtain pose estimates, which are subsequently corrected using line-to-plane correspondences between linear segments in the laser-scan data and orthogonal structural planes of the building. Exploiting the orthogonal building planes ensures fast and efficient initialization and estimation of the map features while providing human-interpretable layout of the environment. The L-INS is experimentally validated by a person traversing a multistory building, and the results demonstrate the reliability and accuracy of the proposed method for indoor localization and mapping.