In this paper, we investigate the multipath resolution problem for direct sequence spread spectrum signals. To resolve multipath components arriving within a very short interval, we propose a new multipath super-resolution algorithm based on the iterative least-squares method. The proposed least-squares-based iterative multipath super-resolution (LIMS) algorithm exploits a triangular shaped auto-correlation function (ACF) of the pseudonoise (PN) sequence and simplifies the least-squares parameter estimation procedure using iterative and algebraic operations. This results in an algorithm demanding low computational load with a high multipath resolution capability. It is also discussed that the LIMS algorithm can be applied for recursive multipath tracking of source localization systems, such as the global navigation satellite systems (GNSS). Simulation results show that the LIMS algorithm maintains its good performance even in a low or severe multipath interference conditions.